| Robert Simson, Euclid - Trigonometry - 1775 - 520 pages
...a quadrant. PROP. XXIII. FIG. 1 6. TN fpherical triangles, whether right angled or oblique angled, **the fines of the fides are proportional to the fines of the** angles oppofite to them. Firft, Let ABC be a right-angled triangle, having a right angle at A ; therefore... | |
| Robert Simson - Trigonometry - 1781 - 466 pages
...affection. i c. PROP. XXTTT. Fie. i6. TN fpherical triangles, whether right-angled of •*- oblique-angled, **the fines of the fides are proportional to the fines of the** angles oppofite to them. Firft, Let ABC be a right-angled mangle, having a right angle at A ; therefore... | |
| David Stewart Erskine Earl of Buchan, Walter Minto - Logarithms - 1787 - 134 pages
...therefore (16) R x fin M = tang Axtang <z=cof Oxcof o. (25) Corollary i. In any fpherical triangle, **the fines of the fides are proportional to the fines of the oppofite angles. For,** in the right angled triangles ADB and CDB (Fig. XIII.), Rxfm BD=fin ABxfm'A, and R x fin BD =fin BC... | |
| John Playfair - Euclid's Elements - 1795 - 400 pages
...two, vk. the ift and Ilth. . . PROP. IN fpherical triangles, whether right angled or oblique angled, **the fines of the fides are proportional to the fines of the** angles oppofite to them. Firft, Let ABC be a right angled triangle, having a right angle at A; therefore,... | |
| Sir Richard Phillips - 1797
...plane triangle, to find SC another fide : this is readily discovered by the well-known theorem, Out **the fides are proportional to the fines of the oppofite angles ; for** this proportion, when wrought, gives rather more than 70 millions of miles for SC, the femidiameter... | |
| Robert Simson - Trigonometry - 1804
...affection. 15. PROP. XXIII. FIG. 1 6. IN fpherical triangles, whether right-angled, or obliqiie* angled, **the fines of the fides are proportional to the fines of the** angles oppofite to them. Firft, Let ABC be a right-angled triangle, having a right angle at A; therefore... | |
| Thomas Leybourn - Mathematics - 1806
...them here as an introduftion to inveftigations which are to follow. 3. Since in fpherical triangles **the fines of the fides are proportional to the fines of the** angles oppofite to them, we may be defirous to inveiligate the conftant ratio, and to difcover if it... | |
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