Gunter's Books of the Cross-Staff
| The First Book of the Cross-Staff |
|
Heading |
Page |
File |
CHAP. I. |
Of the Description of the Cross-Staff |
199 |
2 |
|
1. Description of Lines |
199 |
2 |
CHAP. II. |
The Use of the Line of Inches for perpendicular heights and distances |
202 |
4 |
|
1. To find an height at one Station, by knowing the distance |
202 |
4 |
|
2. To find the height by knowing some part of the same height. |
203 |
4 |
|
3. To find an height at two stations, by knowing the difference of the same stations. |
203 |
4 |
|
4. To find a distance, by knowing the height. |
204 |
5 |
|
5. To find a distance, by knowing part of the height. |
204 |
5 |
|
6. To find a distance at two stations, by knowing the difference of the same stations. |
204 |
5 |
|
7. To find a breadth, by knowing the distanceperpendicular to the breadth. |
205 |
5 |
|
8. To find a breadth at two stations in a Line perpenducular to the breadth, by knowing the difference of the same stations. |
205 |
5 |
CHAP. III. |
The Use of Tangent Lines to taking Angles. |
207 |
6 |
|
1. To find an Angle by the Tangent on the Staff |
207 |
6 |
|
2. To find an Angle by the Tangent of 20 upon the Cross. |
208 |
7 |
|
3. To find an Angle by the Tangent of 30 upon the Cross. |
208 |
7 |
|
4. To observe the altitude of the Sun backward. |
208 |
7 |
|
5. To set the Staff to any Angle given. |
209 |
7 |
|
6. To observe the Altitude of the Sun another way. |
209 |
7 |
|
7. To observe an Altitude by Thread and Plummet. |
209 |
7 |
|
8. To apply the Lines of Inches to the taking of Angles. |
208 |
7 |
CHAP. IV. |
The use of Lines of equal parts joyned with the Lines of Chords. |
210 |
8 |
CHAP. V. |
The Use of the Meridian Line. |
212 |
9 |
CHAP. VI |
The Use of the Line of Numbers. |
216 |
11 |
|
1. Having two numbers given, to find a third in continual proportion, a fourth, a fifth, and so foreward. |
216 |
11 |
|
2. Having two extreme Numbers give,, to find a mean proportional between them. |
217 |
11 |
|
3. To find the square Root of any Number given. |
217 |
11 |
|
4. Having two extreme Numbers given, to find two mean Proportionals between them. |
218 |
12 |
|
5. To find the Cubic Root of a Number given. |
218 |
12 |
|
6. To multiply one number by another. |
218 |
12 |
|
7. To divide one Number by another. |
219 |
12 |
|
8. Three Numbers being given, to find a fourth Proportional. |
219 |
12 |
|
9. Three Numbers being given, to find a fourth in a duplicate proportion. |
219 |
12 |
|
10. Three Numbers being given, to find a fourth in a triplicate proportion. |
220 |
13 |
CHAP. VII. |
The use of the Line of Artifcial Sines. |
221 |
13 |
CHAP. VIII. |
The use of the Line of Artificial Tangents. |
222 |
14 |
CHAP. IX. |
The use of the Line of Sines and Tangents joyned with the Line of Numbers. |
224 |
15 |
|
1. Having three Angles and one side, to find the other two sides. |
224 |
15 |
|
2. Having two sides given, and one Angle opposite to either of these sides, to find the other two Angles and the third side. |
226 |
16 |
|
3. Having two sides and the Angle between them, to find the two other Angles and the third side. |
227 |
16 |
|
4. Having the three sides of a right Line Triangle, to find the three Angles. |
229 |
18 |
|
5. Having the Semidiameter of a Circle, to find the Cord of the Ark. |
230 |
18 |
CHAP. X. |
The use of the Line of versed Sines. |
231 |
18 |
|
|
The Second Book of the Cross-Staff |
233 |
19 |
CHAP. I. |
The use of the Line of Numbers in broad measure, such as Board, Glass, and the like. |
234 |
20 |
SECT. I. |
Of the Mensuration of Oblong Superfacies, and Triangles. |
235 |
20 |
|
1. Having the breadth and length of an Oblong Superfacies given in Inch-measure, to find the content in Inches. |
235 |
20 |
|
2. Having the breadth and length of an Oblong Superfacies given in Inch-measure, to find the content in Feet. |
236 |
21 |
|
3. Having the breadth and length of an Oblong Superfacies given in foot-measure, to find the content in Feet. |
236 |
21 |
|
4. Having the breadth of an Oblong Superfacies given in inches, and the length in foot measure, to find the content in Feet. |
236 |
21 |
|
5. Having the breadth of an Oblong Superfacies given in inches, to find the length of a foot superfacial in inches. |
236 |
21 |
|
6. Having the breadth of an Oblong Superfacies given in feet, to find the length of a foot superfacial in foot measure. |
237 |
21 |
☞ |
7. A four sides Superficies having any of the two sides Parallel, to find the Area. |
237 |
21 |
☞ |
8. To find the Area or content of a Triangle, the longest side and the Perpenducular being given. |
237 |
21 |
☞ |
9. The side of an Equilateral Triangle being given, to find the Area. |
238 |
22 |
☞ |
10. To find the Area of a four sided figure, whose sides are neither equal nor parallel one to the others, which figures are called Trapezias. |
238 |
22 |
☞ |
11. Having the breadth and length of an Oblong Superficies, to find the side of a Square euqla to the Oblong. |
239 |
22 |
SECT. II. |
Of the Mensuration of Regular Polygons. |
240 |
23 |
☞ |
1. The side and the Perpendicular of a Pentagon being given, to find the Area. |
240 |
23 |
☞ |
2. The side and the Perpendicular of an Octagon (or figure of 8 sides) being given, to find the Area. |
241 |
23 |
SECT. III. |
Of the Mensuration of Circles. |
241 |
23 |
☞ |
1. The Diameter of the Circle being given, to find the Circumference. |
241 |
23 |
☞ |
2. The Circumference of a Circle being given, to find the Diameter. |
242 |
24 |
☞ |
3. the Diameter of a Circle being given, to find the Area. |
242 |
24 |
☞ |
4. The Area of a Circle being given, to find the Diameter. |
242 |
24 |
☞ |
5. The Circumference of a Circle being given, to find the Area. |
243 |
24 |
☞ |
6. The Area of a Circle being given, to find the Circumference. |
243 |
24 |
☞ |
7. Having the Diameter of a Circle, to find the side of a Square equal to that Circle. |
243 |
24 |
☞ |
8. Having the Circumference of a Circle, to find the side of a Square equal to the same Circle. |
244 |
25 |
SECT. IV. |
Of the Mensuration of Land by Perch and Acres. |
244 |
25 |
|
1. Having the breadth and length of an Oblong Superfacies given in Perches, to find the content in Perches. |
244 |
25 |
|
2. Having the breadth and length of an Oblong Superfacies given in Perches, to find the content in Acres. |
244 |
25 |
|
A table for the Use of the Chain. |
245 |
25 |
|
3. Having the breadth and length of an Oblong Superfacies given in Chains, to find the content in Acres. |
246 |
26 |
|
4. Having the Perpenducular and Base of a Triangle given in Perches, to find the content in Acres. |
246 |
26 |
|
5. Having the Perpendicular and Base of a Triangle given in Chains, to find the content in Acres. |
246 |
26 |
|
6. Having the content of a Superficies after one kind of Perch, to find the content of the same Superficies, according to another kind of Perch. |
247 |
26 |
|
7. Having the plot of a Plane with the content ion Acres, to find the Scale, by which it was plotted. |
247 |
26 |
|
8. Having the length of a Furlong, to find the breadth of the Acres. |
247 |
26 |
CHAP. III. |
The use of the Line of Numbers in solid measure, such as Stone, Timber, and the like. |
248 |
27 |
SECT. I. |
Of the Mensuration of Regular Solids. |
248 |
27 |
|
1. Having the side of a Square euqal to the base of any Solid given in inch measure, to find the length of a foot Solid in inch measure. |
248 |
27 |
|
2. Having the side of a Square euqal to the base of any Solid given in foot measure, to find the length of a foot Solid in inch measure. |
249 |
27 |
|
3. Having the breadth and depth of a squared Solid given in foot measure, to find the length of a foot solid in foot measure. |
249 |
27 |
|
4. Having the breadth and depth of a squared Solid given in inches, to find the length of a foot solid in inch measure. |
246 |
28 |
|
5. Having the side of a Square equal to the Base of any Solid, and the length thereof given in inch measure, to find the content thereof in feet. |
247 |
28 |
|
6. Having the side of a Square equal to the Base of any Solid, and the length thereof given in foot measure, to find the content thereof in feet. |
247 |
28 |
|
7. Having the side of a Square equal to the Base of any Solid given in inch measure, and the length of the Solid in foot measure, to find the content thereof in feet. |
247 |
28 |
|
8. Having the length, breadth, and depth of a squared Solid given in inches, to find the content in inches. |
248 |
29 |
|
9. Having the length, breadth, and depth of a squared Solid given in inches, to find the content in feet. |
248 |
29 |
|
10. Having the length, breadth, and depth of a squared Solid given in foot measure, to find the content in feet. |
248 |
29 |
|
11. Having the length and breadth of a squared Solid given in inches, and the length in foot measure, to find the content thereof in feet. |
248 |
29 |
SECT. II. |
Of the Mensuration of Cylinders. |
251 |
30 |
|
1. Having the Diameter of a Cylinder given in inch measure, to find the length of a foot Solid in inches. |
251 |
30 |
|
2. Having the Diameter of a Cylinder given in foot measure, to find the length of a foot Solid in foot measure. |
251 |
30 |
|
3. Having the Circumference of e Cylinder given in inches, to find the length of a foot Solid in inch measure. |
251 |
30 |
|
4. Having the Circumference of e Cylinder given in foot measure, to find the length of a foot Solid in inch measure. |
252 |
31 |
|
5. Having the side of a Square equal to the Base of a Cylinder, to find the length of a foot Solid. |
252 |
31 |
|
6. Having the Diameter of a Cylinder, and the length given in inches, to find the content in inches. |
252 |
31 |
|
7. Having the Diameter and length of a Cylinder in foot measure, to find the content in feet. |
253 |
31 |
|
8. Having the Diameter of a cylinder, and the length given in inches, to find the content in feet. |
253 |
31 |
|
9. Having the Diameter of a Cylinder, given in inches, and the length in feet, to find the content in feet. |
253 |
31 |
|
10. Having the Circumference and length of a Cylinder given in inches, to find the content in inches. |
254 |
32 |
|
11. Having the Circumference and length of a Cylinder given in inches, to find the content in feet. |
254 |
32 |
|
12. Having the Circumference and length of a Cylinder given in foot measure, to find the content in feet. |
254 |
32 |
|
13. Having the Circumference of a Cylinder given in inches and the length in foot measure, to find the content in feet. |
254 |
32 |
SECT. III. |
Of the Mensuration of Cones. |
255 |
32 |
☞ |
1. The Diameter of the base and the length of the side of a Cone being give, to find the superficial content thereof. |
255 |
32 |
☞ |
2. The Diameter and Axis of a right Cone being given, to find the Solid Content. |
255 |
32 |
SECT. IV. |
Of the Mensuration of Spheres. |
256 |
33 |
☞ |
1. The Diameter of a Sphere being given, to find the Superficial content. |
255 |
32 |
☞ |
2. The Superficies of a Sphere being given, to find the Axis. |
255 |
32 |
☞ |
3. The Axis of a Sphere being given, to find the Solid Content. |
256 |
32 |
☞ |
4. The Solidity of a Sphere being given, to find the Axis. |
256 |
32 |
SECT. V. |
Of the Mensuration of Prisms. |
257 |
32 |
☞ |
1. To find the Solid content of a Triangular Prism. |
257 |
32 |
☞ |
2. To find the Solid content of a Regular Solid, whose sides at the end thereof are equal and more than 3. As 4, 5, 6, 7, 8, 10 &c. |
258 |
33 |
SECT. VI. |
☞Of the Mensuration of Pyramides. |
259 |
33 |
SECT. VII. |
☞Of the Mensuration of Frustrums or Segments of Pyramides or Cones. |
259 |
33 |
CHAP. IV. |
The use of the Line of Numbers in Gauging of Vessels. |
261 |
35 |
|
1. Having the Diameter and length of a Vessel with the content thereof, to find the Gauge point. |
262 |
36 |
|
2. Having the mean Diameter, and the length of a Vessel, to find the content. |
262 |
36 |
|
3. Having the Diameter and Content, to find the length. |
263 |
36 |
|
4. Having the length of a Vessel, and the content, to find the Diameter. |
263 |
36 |
CHAP. V. |
Containing such Astronomical Propositions as are of ordinary use in the practice of Navigation. |
263 |
36 |
|
1. To find the Altitude of the Sun by the shadows on a Gnomon set Perpendicular to the Horizon. |
263 |
36 |
|
2. Having the distance of the Sun, from the next Equinoctial point, to find his declination |
264 |
37 |
|
3. Having the Latitude of a place, and the Declination of the Sun, to find the time of the Suns rising and setting. |
264 |
37 |
|
4. Having the Latitude of a place, and the distance of the Sun, from the next Equinoctial point, to find his Amplitude. |
265 |
37 |
|
5. Having the Latitude of a place, and the Declination of the Sun, to find his Amplitude. |
265 |
37 |
|
6. Having the Latitude of a place, and the Declination of the Sun, to find the time when the Sun cometh to be due East or West. |
266 |
38 |
|
7. Having the Latitude of a place, and the Declination of the Sun, to find what Amplitude the Sun shall have, when he cometh to be due East or West. |
266 |
38 |
|
8. Having the Latitude of a place, and the Declination of the Sun, to find what Altitude the Sun shall have at the hour of six. |
267 |
38 |
|
9. Having the Latitude of a place, and the Declination of the Sun, to find what Azimtuh the Sun shall have at the hour of six. |
267 |
38 |
|
10. Having the Latitude of a place, and the Declination of the Sun, and the Altitude of the Sun, to find the Azimuth. |
267 |
38 |
|
11. Having the Latitude of a place, and the Declination of the Sun, and the Altitude of the Sun, to find the hour of the day. |
270 |
40 |
|
12. Having the Azimuth, the Suns Altitude, and the Declination, to find the hour of the day. |
271 |
40 |
|
13. Having the hour of the day, the Suns Altitude, and the Declination, to find the Azimuth. |
271 |
40 |
|
14. Having the distance of the Sun from the next Equinoctial point, to find his right Ascension. |
271 |
40 |
|
15 Having the Declination of the Sun, to find his right Ascension. |
272 |
41 |
|
16. Having the Longitude and latitude of a Star, to find the right Ascension of that Star. |
272 |
41 |
|
17. To find the Declination of that Star. |
272 |
41 |
CHAP. VI |
Containing such nautical questions, as are of ordinary use, concerning Longitude, Latitude, Rumb, and Distance. |
280 |
46 |
|
1. To keep an account of the Ships way. |
280 |
46 |
|
2. By the Latitude and differences of Longitude, to find the distance upon a course of East or West. |
282 |
47 |
|
3. By the Latitude and distance upon a course of East or West, to find the difference of Longitude. |
282 |
47 |
|
4. The Longitude and Latitude of two places being given, to find the Rumb leading from the one to the other. |
284 |
48 |
|
6. By the Rumb and both Latitudes, to find the distance upon the Rumb. |
286 |
49 |
|
7. By the distance and both Latitudes to find the Rumb. |
286 |
49 |
|
8. By one Latitude, Rumb, and distance, to find the difference of Latitudes. |
287 |
49 |
|
9. by the Rumb and both Latitudes, to find the difference of Longitude. |
287 |
49 |
|
10. By the Rumb and both Latitudes, to find the distance belonging to the Chart of Mercators Projection. |
288 |
50 |
|
11. By the way of the ship, and two Angles of position, to find the distance between Ship and Land. |
289 |
50 |
|
12. By knowing the distance between two places on the Land, and how they bear one from the other, and having the Angles of Position at the Ship, to find the distance between the Ship and the Land. |
291 |
51 |
PROBL. I. |
The course and distance that the Ship hath run or sailed, being given, to find the true place or point where the Ship is in Mercators Chart. |
294 |
53 |
PROBL. II. |
The course that the Ship hath sailed on, and both Latitudes being know, to find the true place or point that the Ship is on in Mercators Chart, and the true distance that the Ship hath sailed. |
296 |
54 |
PROBL. III |
Both the Latitudes given, and the distance run upon a Course, to find the point or place that the Ship is on in Mercators Chart, and the course or point of the Compass that the Ship hath sailed on. |
296 |
54 |
PROBL. IV. |
Both Latitudes, and the departure or distance of the Meridian you are upon, and the Meridian you began yours course on, to find the point or place where you are in Mercators Chart, also the course that you have made godd, and the distance that you have run from the place, where you began your course. |
297 |
54 |
PROBL. V. |
Both latitudes being given, and the difference of Longitude, to find the distance the Ship hath kept, and the distance it hath run. |
298 |
55 |
PROBL. VI. |
One Latitude, with the course, and the difference of Longitude given, to find the other Latitude, and distance run. |
298 |
55 |
An Appendix |
Concerning the description and use of an Instument, made in form of a Cross-bow, for more easie finding of the Latitude at Sea. |
299 |
55 |
|
1. The day of the month being known, to find the declination of the Sun. |
301 |
56 |
|
2. The declination being given, to find the day of the month. |
301 |
56 |
|
3. To find the Altitude of the Sun, or Star. |
302 |
57 |
|
4. To find any North Latitude, by the Meridian Altitude of the Sun at a forward observation, knowing either the day of the month, or the declination of the Sun. |
302 |
57 |
|
5. To find any North latitude, by the Meridian Altitude of the Stars to the Southward. |
303 |
57 |
|
6. To find any North latitude, by the Meridian Altitude of the Stars to the Northward. |
303 |
57 |
|
7. To find any South Latitude, by the Meridian Altitude of the Sun at a forward observation, knowing either the day of the month, or the declination of the Sun. |
305 |
58 |
|
8. To find any South latitude by the Meridian Altitude of the Stars to the Northward. |
305 |
58 |
|
9. To observe the Altitude of the Sun by the Bow, or with an Astrolabe. |
305 |
58 |
|
10. To find the South latitude by the Meridian Altitude of the Stars to the Southward. |
306 |
59 |
|
11. To observe the Altitude of the Sun backward. |
306 |
59 |
|
12. To find any North Latitude by the Meridian Altitude of the Sun at a back observation, knowing either the day of the month, or the declination of the Sun. |
307 |
59 |
|
13. To find any South Latitude by the Meridian Altitude of the Sun at a back observation, knowing either the day of the month, or the declination of the Sun. |
307 |
59 |
|
14. To find the day of the month, by knowing the Latitude of the place, and observing the Meridian Altitude of the Sun. |
308 |
60 |
|
15. To find the declination of any unknown Star, and so to place it on the Bow, knowing the Latitude of the place, and observing the Meridian Altitude of the Star. |
308 |
60 |
|
16. To find any North latitude on land by observation with Thread and Plummet. |
308 |
60 |
|
17. To find any Latitude on Land, by observation with Thread and Plummet. |
309 |
60 |
☞ |
(Table of) The right Ascension of these Stars is to the year 1670. |
309 |
60 |
|
FINIS |
311 |
61 |
|
The Third Book of the Cross-Staff |
|
The use of the Line of Numbers, Sines and Tangents for the drawing of Hour-lines on all sorts of Planes. |
1 |
1 |
|
To describe the Fundamental Diagram |
3 |
2 |
|
To find the Inclination of any Plane. |
5 |
3 |
|
To find the Declination of a Plane. |
6 |
4 |
CHAP. I. |
To draw the Hour-lines in an Equinoctial plane. |
9 |
5 |
CHAP. II. |
To draw the Hour-lines in a Direct Polar Plane. |
10 |
6 |
CHAP. III. |
To draw the Hour-lines in a Meridian Plane |
14 |
8 |
CHAP. IV. |
To draw the Hour-lines in an Horizontal Plane. |
15 |
8 |
CHAP. V. |
To draw the Hour-lines in a Vertical Plane. |
19 |
10 |
CHAP. VI. |
To draw the Hour-lines in a Vertical Inclining Plane. |
21 |
11 |
CHAP. VII. |
To draw the Hour-lines in a Vertical Declining Plane. |
24 |
12 |
|
1. To find the Height of the Pole above the Plane. |
26 |
14 |
|
2. To find the Distance of the Substylar from the Meridian. |
26 |
14 |
|
3. To find the Distance of each Hour-line from the Substylar. |
27 |
14 |
|
4. To find the Inclination of the Meridians. |
26 |
15 |
|
A Second Example |
31 |
17 |
|
A Third Example, of a Plane falling near a Meridian. |
32 |
17 |
CHAP. VIII. |
To draw the Hour-lines in a Meridian Inclining Plane. |
37 |
19 |
CHAP. IX. |
To describe the Hour-lines in a Polar Declining Plane. |
42 |
22 |
|
1. The Ark of the Plane between the Horizon and the Pole. |
43 |
22 |
|
2. The Installation of the Meridian of the Plane to the Meridian of the Place. |
44 |
23 |
CHAP. X. |
To draw the Hour-lines in a Declining Inclining Plane. |
47 |
24 |
|
A Second Example of a Plane falling between the Pole and the Zenith. |
53 |
27 |
|
A Third Example of a Plane Inclining to the Southward. |
54 |
28 |
CHAP. XI. |
To Describe the Tropicks and other Circles of Declination in an Equinoctial Plane. |
55 |
28 |
CHAP. XII. |
To Describe the Tropicks and other Circles of Declination in a Polar Plane. |
57 |
29 |
CHAP. XIII. |
To Describe the Tropicks and other Circles of Declination in such a Plane as is neither Equinoctial nor Polar. |
63 |
32 |
|
1. To Proportion the Style unto the Plane. |
65 |
33 |
|
2. Having the Length of the Axis, and the Height of the Style above the Plane, to find the Length of the Sides of the Style. |
67 |
34 |
|
3. To find the Distance between the Center and the Equator upon the Substylar Line. |
67 |
34 |
|
4. To find the Angles contained between the Equator and the Hour-lines upon your Plane. |
68 |
35 |
|
5. To find the Distance between the Center and the Parallels of Declination. |
69 |
35 |
CHAP. XIV. |
To Describe the Parallels of the Sines in any of the former Planes. |
71 |
36 |
CHAP. XV. |
To Describe the Parallels of the length of the Day in any of the former Planes. |
71 |
36 |
CHAP. XVI. |
To draw the Old Unequal Hours in the former Planes. |
74 |
38 |
CHAP. XVII. |
To draw the Hours from Sun-rising to Sun-setting in the former Planes. |
76 |
39 |
CHAP. XVIII. |
To draw the Horizontal Line in the former Planes. |
77 |
39 |
CHAP. XIX. |
To Describe the Vertical Circles in the former Planes. |
79 |
40 |
|
1. To find the distance between the Foot of the Style and the Vertical Point. |
81 |
42 |
|
2. To find the distance between the Foot of the Style and the Horizontal-line. |
82 |
42 |
|
3. To find the Angles made by the Azimuth-lines at the Vertical Point. |
82 |
42 |
CHAP. XX. |
To Describe the Parallels of the Horizon in the former Planes. |
85 |
43 |
|
1. To find the distance between the top of the Style, and the several Points wherein the Azimuths do cross the Horizontal-lines. |
|
44 |
|
2. To find the distance between the Horizon and the Paralles. |
89 |
45 |
|
1. To find the length of the Axis of the Horizon. |
91 |
46 |
|
2. To find the Angles contained between the Horizon and the Vertical Lines upon the Plane. |
91 |
46 |
|
3. To find the distance between the Vertical Points, and the Parallel of the Horizon. |
94 |
48 |
|
4. To describe such Parallels on the former Planes, as may shew the proportion of the Shadow unto the Gnomon. |
95 |
49 |
An Appendix concerning the Description and Use of a small Portable Quadrant, For the more easie finding of the Hour and Azimuth, and other Astronomical and Geometrical Conclusions. |
96 |
49 |
CHAP. I. |
Of the Description of the Quadrant. |
97 |
49 |
CHAP. II. |
Of the Use of the Quadrant, in taking the Altitude of the Sun, Monn, and Stars. |
113 |
57 |
CHAP. III. |
Of the Ecliptick. |
114 |
58 |
|
1. The Place of the Sun being given, to find the Right Ascension. |
114 |
58 |
|
2. The Right Ascension being give, to find his Place to the Ecliptick. |
114 |
58 |
CHAP. IV. |
Of the Line of Declination. |
115 |
58 |
|
1. The Place of the Sun being given, to find his Declination. |
115 |
58 |
|
2. The Declination of the Sun being given, to find his Place in the Ecliptick. |
115 |
58 |
CHAP. V. |
Of the Circle of Months and Days. |
115 |
58 |
|
1. The Day of the Month being give, to find the Altitude of the Sun at Noon. |
116 |
59 |
|
2. The Meridian Altitude being given, to find the day of the Month. |
116 |
59 |
CHAP. VI. |
Of the Hour-lines. |
117 |
59 |
|
1. The day of the Month, or the Height at Noon being known, to find the Place of the Sun in the Ecliptick. |
117 |
59 |
|
2. The Place of the Sun in the Ecliptick being known, to find the Day of the Month. |
118 |
60 |
|
3. The Hour of the day being given, to find the Altitude of the Sun above the Horizon. |
118 |
60 |
|
4. The Altitude of the Sun being given, to find the Hour of the day. |
120 |
60 |
|
5. The Hour of the Night being given, to find how much the Sun is below Horizon. |
120 |
60 |
|
6. The Depression of the Sun supposed, to give the Hour of the Night with us, or the Hour of the Day to our Antipodes. |
120 |
61 |
|
7. The time if the Year, or the place of the Sun being given, to find the beginning of Day-break, and the end of Twiligth. |
120 |
61 |
CHAP. VII. |
Of the Horizon. |
121 |
61 |
|
1. The Day of the Month, or the Place of the Sun being known, to find the Amplitude of the Suns Rising and Setting. |
121 |
62 |
|
2. The Day of the Month, or the Place of the Sun being given, to find the Ascensional Difference. |
121 |
61 |
CHAP. VIII. |
Of the Five Stars. |
122 |
62 |
|
The Altitude of any of these five Stars being known, to find the Hour of the Night. |
122 |
62 |
CHAP. IX. |
Of the Azimuth-lines. |
124 |
63 |
|
1. The Azimuth whereupon the Sun beareth from us being known, to find the Altitude of the Sun above the Horizon. |
124 |
63 |
|
2. The Altitude of the Sun being given, to find on what Azimuth he beareth from us. |
125 |
63 |
CHAP. X. |
Of the Quadrat. |
125 |
63 |
|
1. Any point being given, to find whether it is level with the Eye. |
126 |
64 |
|
2. To find an Height above the Level of the Eye, or a Distance at one observation. |
126 |
64 |
|
3. To find a Height, or a Distance at two Observations. |
127 |
64 |
A Second Appendix Concerning the Description and Use of another Quadrant, fitted for daily Practice; For finding the Hour and Azimuth, and other things.... |
128 |
64 |
Invented by Mr. Sam. Foster |
129 |
65 |
|
The Description of the Quadrant |
129 |
65 |
|
How to Inscribe the Additional Lines upon the Quadrant |
131 |
66 |
|
1. For the Lines on the Fortside. |
131 |
66 |
|
2. For the Lines on the Backside. |
133 |
67 |
|
The Uses of the Quadrant. |
135 |
68 |
|
1. To find the Suns Declination. |
135 |
68 |
|
2. To rectifie the Bead for Observation of Hour or Azimuth; and to perform those things that are done by the usual Lines upon the Quadrant. |
136 |
69 |
|
3. To find when Twilight begins in the Morning, and ends at Evening; which Moments are the two utmost Terms of Dark Night. |
138 |
70 |
|
4. To find the Suns Ascensional Difference &c. |
139 |
70 |
|
5. To find the Suns Amplitude, &c. |
139 |
70 |
|
6. Having the Declination of an upright Plane, to find the elevation of the Style, &c. |
139 |
70 |
|
7. To find the Deflection, &c. |
140 |
71 |
|
8. To find the Difference of Longitude, &c. |
140 |
71 |
|
9. To make an Horizontal Dial. |
140 |
71 |
|
10. To find what Angle any Hour-circle maketh with the Horizon, or any Azimuth maketh with the Equinoctial. |
141 |
71 |
|
11. To find what Ark of any Hour-circle is intercepted between the Equinoctial (or any Parallel) and the Horizon. |
141 |
71 |
|
12. How high the Sun shall be upon any Azimuth, and in any Declination. |
142 |
72 |
|
13. To find how high the Sun shall be at any Hour, and in any Declination. |
144 |
73 |
|
14. To find the Suns Azimuth. |
144 |
73 |
|
15. To find the Hour of the Day by the Sun. |
146 |
74 |
|
16. To find the Declination of a Plane. |
147 |
74 |
|
17. How to draw an upright declining Dial. |
148 |
75 |
|
18. Of the upright full South-Dial. |
150 |
76 |
|
19. Of upright far declining Planes. |
150 |
76 |
|
20. Concerning the forming and the placing of the Stile. |
152 |
77 |
|
21. Of the East and West upright Dial. |
154 |
78 |
|
For the Stile. |
154 |
78 |
|
22. In East and West Re-incliners, to get the Deflection. |
156 |
79 |
|
23. To find the Angle between 12 and 6. |
156 |
79 |
|
24. To get the Stiles elevation. |
156 |
79 |
|
25. To find the Difference of Longitude. |
156 |
79 |
|
26. How to draw the Dial. |
157 |
79 |
|
27. To make the Horizontal Dial to any Latitude. |
158 |
80 |
|
28. To find the Hour of the Night by the Stars. |
159 |
80 |
|
To use the Altrimetrick Scale |
161 |
81 |
|
1. To find any Height at one Observation. |
161 |
81 |
|
2. To find part of an Altitude. |
162 |
82 |
|
3. Standing upon a known Height to find a Distance. |
162 |
82 |
|
4. To find part of a Distance. |
163 |
82 |
|
5. To find a Height at two Observation. |
163 |
82 |
|
Finis |
164 |
83 |
|
[zurück zur Übersicht]
|