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" C' (89) (90) (91) (92) (93) 112. In any plane triangle, the sum of any two sides is to their difference as the tangent of half the sum of the opposite angles is to the tangent of half their difference. "
A Treatise of Practical Surveying, ... - Σελίδα 94
των Robert Gibson - 1808 - 440 σελίδες
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A Treatise of Algebra in Two Books: The First Treating of the Arithmetical ...

Philip Ronayne - 1717 - 478 σελίδες
...С : : 5, С • S, A " - S,C: 3 D) == S, A, QED' AXIOM AXIOM. III. The Sum of che Legs of an Angle is to their Difference as the Tangent of half the Sum of the Angles oppofite to rhofe Legs, is to the Tangent of half their Difference. Demonßrütion. „ In the...

The Doctrine of Plain and Spherical Trigonometry: With Its Application and ...

William Hawney - 1725 - 504 σελίδες
...the Tangent of half their Difference. But Wholes are as their Halves : Therefore the Sum of the Legs is to their Difference, as the Tangent of half the Sum of the oppofite Angles, is to the Tangent of half their Difference. Which was, &c. From this Axiom the following...

The Young Mathematician's Guide: Being a Plain and Easy Introduction to the ...

John Ward (of Chester.) - 1747 - 516 σελίδες
...the Tangent of half their Difference : But Wholes are as their Halves ; wherefore the Sum of the Legs is to their Difference, as the Tangent of half the Sum of the Angles oppofice is to the Tangent of half their Difference. j£. ED Axiom IV. -4. The Bale, or greateu...

The Mathematician

1751 - 420 σελίδες
...writers of Trigonometry, that the Sum of the Sides, including any given Angle Angle of a plain Triangle, is to their Difference, as the Tangent of half the Sum of the unknown Angles, is to the Tangent of half their Difference ; therefore, if the including Sides of two...

A Treatise of Practical Surveying: Which is Demonstrated from Its First ...

Robert Gibson - 1795 - 384 σελίδες
...AH : IH : : CE : ED, that is, as the Sum of the two Sides AB and BC, is to their Difference ; fo is the Tangent of half the Sum of the two unknown Angles A and C, • to the Tangent of half their Difference. QED THEO. Plate V. <THE 0. III. In any right-lined plane...

A Treatise of Practical Surveying: Which is Demonstrated from Its First ...

Robert Gibson - 1806 - 486 σελίδες
...AH : IH : : CE : ED, that is .as the sum of the two sides AB and BC, is to their difference ; so is the tangent of half the sum of the two unknown angles A and C, to the tangent of half their difference. QED 104 PLANE TRIGONOMETRY. Plate V. THEOREM JII. In any right-lined...

The Elements of Euclid: The Errors, by which Theon, Or Others, Have Long Ago ...

Robert Simson - 1806 - 546 σελίδες
...given, the fourth is also given. ' PROP. III. FIG. 8. In a plane triangle, the sum of any two sides is to their difference, as the tangent of half the sum of the angles at the base, to the tangent of half their difference. . * Let ABC be a plane triangle, live...

A Treatise on Plane and Spherical Trigonometry: With Their Most Useful ...

John Bonnycastle - 1806 - 464 σελίδες
...circle is to the radius of the tables. THEOREM II. 94. The sum of any two sides of a plane triangle ABC, is to their difference, as the tangent of half the sum of their opposite angles is to the tangent of half their difference. . &> For about one of the angular...

Elements of Geometry, Geometrical Analysis, and Plane Trigonometry: With an ...

Sir John Leslie - 1809 - 522 σελίδες
...dt 3"-V zp: « <f-*s"-*+n. n -- * 3 2 -7 s -6 &c . PROP. IV. THEOR. The sum of the sines of two arcs is to their difference, as the tangent of half the sum of the arcs to the tangent of half the difference. If A and B denote two arcs; the S,A + S,B : S, A — S,B...

The Elements of Euclid: Viz. the First Six Books, Together with the Eleventh ...

Euclid - 1810 - 554 σελίδες
...of half their difference. • Let ABC be a plane triangle, the sum of any two sides, AB, AC will be to their difference as the tangent of half the sum of -;' the angles at the base ABC, ACB to the tangent of half their difference. About A as a centre, with AB the...




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