 The First Book of the CrossStaff 

Heading 
Page 
File 
CHAP. I. 
Of the Description of the CrossStaff 
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 CrossStaff 
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 Inchmeasure, to find the content in Inches. 
235 
20 

2. Having the breadth and length of an Oblong Superfacies given in Inchmeasure, to find the content in Feet. 
236 
21 

3. Having the breadth and length of an Oblong Superfacies given in footmeasure, 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 Crossbow, 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 CrossStaff 

The use of the Line of Numbers, Sines and Tangents for the drawing of Hourlines 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 Hourlines in an Equinoctial plane. 
9 
5 
CHAP. II. 
To draw the Hourlines in a Direct Polar Plane. 
10 
6 
CHAP. III. 
To draw the Hourlines in a Meridian Plane 
14 
8 
CHAP. IV. 
To draw the Hourlines in an Horizontal Plane. 
15 
8 
CHAP. V. 
To draw the Hourlines in a Vertical Plane. 
19 
10 
CHAP. VI. 
To draw the Hourlines in a Vertical Inclining Plane. 
21 
11 
CHAP. VII. 
To draw the Hourlines 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 Hourline 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 Hourlines in a Meridian Inclining Plane. 
37 
19 
CHAP. IX. 
To describe the Hourlines 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 Hourlines 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 Hourlines 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 Sunrising to Sunsetting 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 Horizontalline. 
82 
42 

3. To find the Angles made by the Azimuthlines 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 Horizontallines. 

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 Hourlines. 
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 Daybreak, 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 Azimuthlines. 
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 Hourcircle maketh with the Horizon, or any Azimuth maketh with the Equinoctial. 
141 
71 

11. To find what Ark of any Hourcircle 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 SouthDial. 
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 Reincliners, 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 

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