Geometrical trigonometry, or, The explanation of such geometrical problems as are most useful & necessary, either for the construction of the canons of triangles, or for the solution of them together with the proportions themselves suteable unto every case both in plain and spherical triangles ... / by J. Newton ...

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Title
Geometrical trigonometry, or, The explanation of such geometrical problems as are most useful & necessary, either for the construction of the canons of triangles, or for the solution of them together with the proportions themselves suteable unto every case both in plain and spherical triangles ... / by J. Newton ...
Author
Newton, John, 1622-1678.
Publication
London :: Printed for George Hurlock ... and Thomas Pierrepont ...,
1659.
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Subject terms
Trigonometry -- Early works to 1800.
Link to this Item
http://name.umdl.umich.edu/A52262.0001.001
Cite this Item
"Geometrical trigonometry, or, The explanation of such geometrical problems as are most useful & necessary, either for the construction of the canons of triangles, or for the solution of them together with the proportions themselves suteable unto every case both in plain and spherical triangles ... / by J. Newton ..." In the digital collection Early English Books Online. https://name.umdl.umich.edu/A52262.0001.001. University of Michigan Library Digital Collections. Accessed June 15, 2025.

Pages

Illustration by Logarithmes.

 Logarithmes.
As the leg AC 143.72 2.157517
Is to the rad. IC 10.0000
So is the leg AB 235 2.371068
To the tang. of. C. gr. 58.5510.213551

2 Probl. The angles and one leg gi∣ven, to find the other leg.

In the right angled plain Triangle ABC, the leg AC is inquired:

The given

  • Angle ABC
  • Leg. AB
Rad. AB▪ ∷ t ABC. AC. by the first Axiome.

Page 61

3 Prob. The Hypotenuse and a leg given to find an angle.

In the right angled plain Triangle ABC, the angle ACB is inquired.

The given

  • Hypoth. BC.
  • Leg AB.

BC. Rad ∷ AB. s. ACB. by 2 Ax.

4 Probl. The Hypotenuse and angles given, to find either leg.

In the right angled plain Triangle ABC, the leg. AB is inquired:

The given

  • Hypot. BC.
  • Angle ACB.

Rad. BC ∷ s. ACB. AB. by 2 Ax.

5 Probl. The angles and a leg gi∣ven, to find the Hypotenuse.

In the right-angled plain Triangle ABC, the Hypotenuse BC is inquired;

The given

  • Angle ABC.
  • The given Leg AC.

s. ABC. AC ∷ Rad. BC. by the se∣cond Axiome.

Page 62

6 Probl. The Hypotenuse and leg given, to find the other leg.

In the right-angled plain Triangle ABC, the leg AB is inquired,

The given

  • Hypot. BC
  • Leg. AC

1. BC. Rad ∷ AC. s. ABC, by the 3 Problem.

2. t. ABC. AC ∷ Rad. AB. by the 2 Probl.

7 Probl. The legs given, to find the Hypotenuse.

In the right-angled plain Triangle ABC the Hypotenuse BC is inquired.

The given legs

  • AB
  • AC

1 AB. Rad ∷ AC. t. ABC by the 1 Problem.

2 s. ABC. AC ∷ Rad. BC. by the 5 Problem.

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