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" II, (Art. 144.) the sum of the sides is to their difference ; as the tangent of half the sum of the opposite angles, to the tangent of half their difference. Therefore, R : tan (ACH— 45°) : : tan £(ACB+B) : tan i(ACB-B) Ex. "
The Mathematical Questions Proposed in the Ladies' Diary: And Their Original ... - الصفحة 309
بواسطة Thomas Leybourn - 1817
عرض كامل - لمحة عن هذا الكتاب

Collection of English Almanacs for the Years 1702-1835

1798 - عدد الصفحات: 410
...Eti. IVarrc* . When' the verfiele ar.jle of any plan: triangle is bifeñcd ; the Гц m of the fides is to their difference, as the tangent of the angle made by the bilecVmg line and fcafe , is to the tangent of half th: vertí tal angle. Required a demonftration....

Easy Introduction to Mathematics, المجلد 2

Charles Butler - 1814 - عدد الصفحات: 582
...AED are equiangular (29. 1.), v AF : FB : : AE : ED (4. 6.) and AF : AE:: FB : ED (16. 5.) ; 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. QED When two sides...

The Elements of Euclid; viz. the first six books, together with the eleventh ...

Euclides - 1814 - عدد الصفحات: 560
...and CF their difference; and since BC, FG 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, tothe tangent of half their difference. •'• - °" •'...

A Treatise of Plane Trigonometry: To which is Prefixed, a Summary View of ...

Jeremiah Day - 1815 - عدد الصفحات: 172
...construction, equal to the sum, and FH to the difference of AC and AB. And by theorem II, [Art. 144.] the sum of the sides is to their difference ; as the tangent of half the sum of the opposite angles, to the tangent of half their difference. Therefore, R:Tan (ACH-45°;::Tan...

A Practical Application of the Principles of Geometry to the Mensuration of ...

Jeremiah Day - 1815 - عدد الصفحات: 388
...construction, equal to the sum, and FH to the difference of AC and AB. And by theorem II, [Art. 144.] the sum of the sides is to their difference ; as the tangent of half the sum of the opposite angles, to the tangent of half their difference. Therefore, R:Tan (ACH-45°;::Tan...

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

Euclides - 1816 - عدد الصفحات: 588
...and CF their difference; and since BC, FG 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....

New Series of The Mathematical Repository, المجلد 4

Thomas Leybourn - 1819 - عدد الصفحات: 430
...oi : Q o X oq : : BC* : AC*. Required a 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...

The Second [-fifth and Sixth] Part of A Course of Mathematics: Adapted to ...

Jeremiah Day - 1824 - عدد الصفحات: 440
...construction, equal to the sum, and FH to the difference of AC and AB. And by theorem II, [Art. 144.] the sum of the sides is to their difference ; as the tangent of half the sum of the opposite angles, to the tangent of half their difference. Therefore, R : Tan (ACH-450):...

The New American Practical Navigator: Being an Epitome of Navigation ...

Nathaniel Bowditch - 1826 - عدد الصفحات: 732
...angle C. LIX. In any triangle (supposing any side to be the basr, and calling the other two the sides) the sum of the sides is to their difference, as the tangent of half the sum of the angles at the base is to the tangent of half the difference of the tame angles....

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

Robert Simson - 1827 - عدد الصفحات: 546
...and CF their difference ; and since BC, FG 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....




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