CHAP. I. 
Concerning the Use of the Line of Numbers 
166 
002 
Prop. I. 
To multiply one Number by another. 
166 
002 
PROP. II. 
To divide one Number by another. 
167 
002 
PROP. III. 
To find the Square of a Number. 
168 
003 
PROP. IV. 
To find the Cubique Root of a Number. 
168 
003 
PROP. V. 
Three Numbers being given, to find a fourth Proportional. 
169 
003 
PROP. VI. 
Three Numbers being given, to find a fourth in a duplicated Proportion. 
172 
005 
PROP. VII. 
Three Numbers being given, to find a fourth in a triplicated Proportion. 
174 
006 
PROP. VIII. 
Having two Numbers given, to find a third in continual Proportion, a fourth, a fifth, a sixth, and so forward. 
175 
006 
PROP. IX. 
Having two extreme Numbers given, to find a mean Proportional between them. 
179 
008 
PROP. X. 
Having two extreme Numbers given, to find two mean Proportionals between them. 
179 
008 
CHAP. II. 
Concerning the Use of the Lines of Sines and Tangents in the resolving of Spherical Triangles. 
182 
010 

In a RECTANGLE TRIANGLE. 
184 
011 

1. To find a Side by knowing the Base and the Angle opposite to the required Side. 
184 
011 

2. To find a Side by knowing the Base and the other Side. 
184 
011 

3. To find a Side by knowing the two Oblique Angles. 
185 
011 

4. To find the Base by knowing both the Sides. 
185 
011 

5. To find the Base by knowing one Side and the Angle opposite to that Side. 
185 
011 

6. To find an Angle by knowing the other Oblique Angle, and the Side opposite to the Angle required. 
186 
012 

7. To find an Angle by knowing the other Oblique Angle, and the Side opposite to the Angle given. 
186 
012 

8. To find an Angle by knowing the base, and the Side opposite to the Angle required. 
186 
012 

9. To find a Side, by knowing the other Side, and the Angle opposite to the Side required. 
187 
012 

10. To find a Side, by knowing the other Side, and the Angle next to the Side required. 
187 
012 

11. To find a Side, by knowing the Base, and the Angle next to the Side required. 
187 
012 

12. To find the Base by knowing both Oblique Angles. 
188 
013 

13. To find the Base by knowing one of the Sides and the Angle next to that Side. 
188 
013 

14. To find an Angle by knowing both Sides. 
188 
013 

15. To find an Angle by knowing the Base, and the Side next to the Angle required. 
189 
013 

16. To find an Angle by knowing the Base, and the other Oblique Angle. 
189 
013 

In any SPHERICAL TRIANGLE. 
189 
013 

17. To find a Side opposite to an Angle, by knowing one Side and two Angles, the one opposite to the Side given, the other to the Side required. 
189 
013 

17. To find a Side opposite to an Angle, by knowing one Side and two Angles, the one opposite to the Side given, the other to the Side required. 
190 
014 

18. To find an Angle opposite to a Side, by knowing one Angle and two Sides, the one opposite to the Angle given, the other to the Angle required. 
190 
014 

19. To find an Angle by knowing the three Sides. 
190 
014 

20. To find a Side by knowing the three Angles. 
192 
015 

21. To find a Side by the other two Sides and the Angle comprehended. 
193 
015 

22. To find a Side by knowing the other two Sides and one Angle next to the Side required. 
194 
016 

23. To find a Side by knowing one Sides and the two Angle next to the second Side. 
194 
016 

24. To find a Side by knowing two Angle and the Side inclosed by them. 
195 
016 

25. To find an Angle by knowing the other two Angles and one Side next to the Angle required. 
195 
016 

27. To find an Angle by knowing tow Sides and the Angles contained by them. 
196 
017 

28. To find an Angle by knowing two next Sides, and one of the other Angles. 
196 
017 

29. To find a Side, by knowing the other two Sides, and their opposite Angle. 
197 
017 

30. To find an Angle, by knowing the other two Angles, and their opposite Sides. 
197 
017 
CHAP. III. 
Concerning the joyned Use of the Line of Numbers, Sines and Tangents. 
198 
018 
Prop. I. 
Having three Angles and one Side, to find the other two Sides. 
198 
018 
Prop. II. 
Having two Sides and one Angle opposite to either of those Sides, to find the other two Angles and the third Side. 
199 
018 
Prop. III. 
Having two Sides, and the Angle between them, to find the other two Angles and the third Side. 
201 
019 
Prop. IV. 
Having three Sides, to find the three Angles. 
202 
020 
Prop. V. 
Having the Base and Perpendicular in a rightlined Triangle, to find the superficial Content. 
203 
020 
Prop. VI. 
Having two Sides of a rightlined Triangle, and the Angle between them, to find the Content. 
204 
021 
Prop. VII. 
Having three Angles, and one Side of a rightlined Triangle, to find the Content. 
204 
021 
Prop. VIII. 
Having three Sides of a rightlined Triangle, to find the Content. 
205 
021 
Prop. IX. 
Having three Sides of a rightlined Triangle, to find the Perpendicular. 
205 
021 
Prop. X. 
Having the Semidiameter of a Circle, to find a Chord for any Ark proposed. 
206 
022 
CHAP. IV. 
Containing some Use of rightlined Triangles in the Practice of FORTIFICATION. 
207 
022 
Prop. I. 
Having the Side of a Regular Fort, with the length of the Gorge, the Flank and the Face of the Bulwark, to find the rest of the Lines and Angles. 
207 
022 
Prop. II. 
Having the ordinary Angles, with the Flank and Line of Defence, to find the rest of the Lines and Angles in a Regular Fort. 
212 
025 
Prop. III. 
Having the ordinary Angles, with the Line of Defence and Face of the Bulwark, to find the rest of the Lines and Angles in a Regular Fort. 
217 
027 
Prop. IV. 
Having the Angles of an irregular Fort, with the Sides between them, and the face of the Bulwark, to find the rest of the Lines and Angles. 
219 
028 
Prop. IV. 
Having the lines and Angles of a Regular Fort, to find the Content in Feet and Acres. 
223 
030 


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