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" In any plane triangle, as the sum of the sides about the vertical angle is to their difference, so is the tangent of half the sum of the angles at the base to the tangent of half their difference. "
Practical Surveying: A Text-book for Students Preparing for Examinations Or ... - Seite 116
von George William Usill - 1889 - 272 Seiten
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The Elements of Euclid: The Errors, by which Theon, Or Others, Have Long Ago ...

Robert Simson - 1806 - 548 Seiten
.... * Let ABC be a plane triangle, live sura of any two sides, AB, AC will be to their difiV.-rt.-nce 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 greater side for...
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Elements of Geometry, Geometrical Analysis, and Plane Trigonometry ...

Sir John Leslie - 1809 - 542 Seiten
...AB : BC :: S,C : S, A. PROP. X. THEOR. In any triangle, the sum of two sides, is to the difference, as the tangent of half the sum of the angles at the base, to the tangent of half their difference. In the triangle ABC, AB + AC : AB-AC : : T,°-±?: 2 IT" O—...
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The Modern Preceptor ; Or, a General Course of Education, Band 1

John Dougall - 1810 - 732 Seiten
...to EF; AD, however, is the sum of the sides, and AE their difference; while DC was shown above to be the tangent of half the sum of the angles at the base, and EF is the tangent of rulf their difference ; the proposition is, therefore, demonstrated. PROP....
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Institutes of Natural Philosophy: Theoretical and Practical

William Enfield - 1811 - 476 Seiten
...triangle SRM, the sides RS, RM, being thus found, the sum of the two sides RS, RM, is to their difference, as the tangent of half the sum of the angles at the base RSM, RMS, is to the tangent of half their difference. To half the sum add half the difference, and...
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Easy Introduction to Mathematics, Band 2

Charles Butler - 1814 - 582 Seiten
...the preceding article. 72. 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 the difference. Let ABC be a triangle, from € as a centre with the least...
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The Elements of Euclid: Viz. the First Six Books, Together with the Eleventh ...

Euclides - 1816 - 592 Seiten
...are parallel (2. 6.), EC is to CF, as EB to BG; that is, the sum of the 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. PROP. IV. FIG. 18. IN any plane triangle BAG, whose two sides...
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Elements of Plane and Spherical Trigonometry: With Their Applications to ...

Olinthus Gregory - 1816 - 278 Seiten
...triangle it will be, as the sum of the sides about the vertical angle, is to their difference, so is the tangent of half the sum of the angles at the base, to the tangent of half their difference. By the preceding prop. AC : BC :: sin B : sin A, .-. by comp....
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Elements of Geometry and Plane Trigonometry: With an Appendix, and Copious ...

Sir John Leslie - 1817 - 456 Seiten
...supplement are the same. PROP. X. THEOR. In any triangle, the sum of two sides, is to the difference, as the tangent of half the sum of the angles at the base, to the tangent of half their difi ference. In the triangle ABC, AB+AC : AB— AC : : From the vertex...
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Elements of Geometry: Containing the First Six Books of Euclid, with a ...

John Playfair - 1819 - 348 Seiten
...then will the radius be to the tangent of the difference between that angle and half a right angle, as the tangent of half the sum of 'the angles at t,he base of the triangle to the tangent of half their difference. Let ABC be a triangle, the sides of which are BC and CA, and...
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New Series of The Mathematical Repository, Band 4

Thomas Leybourn - 1819 - 444 Seiten
...proof. 8. Prove, geometrically, that in any plane triangle, the sum of the 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. 9. Shew that tan.3 60 = 3 tan. 60 to rad. == i. 10. P and...
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