Elements of Geometry: Containing the First Six Books of Euclid: With a Supplement on the Quadrature of the Circle, and the Geometry of Solids: to which are Added, Elements of Plane and Spherical TrigonometryLippincott, Grambo & Company, 1854 - 317 páginas |
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Página 9
... Spherical Trigonometry John Playfair. ' BD , is named the angle ABD , or DBA ; and that which is contained by ' BD , CB , is called the angle DBC , or CBD ; but , if there be only one an- ' gle at a point , it may be expressed by a ...
... Spherical Trigonometry John Playfair. ' BD , is named the angle ABD , or DBA ; and that which is contained by ' BD , CB , is called the angle DBC , or CBD ; but , if there be only one an- ' gle at a point , it may be expressed by a ...
Página 14
... Spherical Trigonometry John Playfair. coinciding with DE , AC shall coincide with DF , because the angle BAC is equal to the angle EDF ; wherefore also the point C shall coincide with the point F , because AC is equal to DF : But the ...
... Spherical Trigonometry John Playfair. coinciding with DE , AC shall coincide with DF , because the angle BAC is equal to the angle EDF ; wherefore also the point C shall coincide with the point F , because AC is equal to DF : But the ...
Página 15
... Spherical Trigonometry John Playfair. base of the triangle ABC : And it has also been proved that the angle FBC is equal to the angle GCB , which are the angles upon the other side of the base . COROLLARY . Hence every equilateral ...
... Spherical Trigonometry John Playfair. base of the triangle ABC : And it has also been proved that the angle FBC is equal to the angle GCB , which are the angles upon the other side of the base . COROLLARY . Hence every equilateral ...
Página 16
... Spherical Trigonometry John Playfair. but it has been demonstrated to be greater than it ; which is impossi ble ... angle ECD is greater than the angle BCD ; wherefore the angle FDC is likewise greater than BCD ; much more then is the ...
... Spherical Trigonometry John Playfair. but it has been demonstrated to be greater than it ; which is impossi ble ... angle ECD is greater than the angle BCD ; wherefore the angle FDC is likewise greater than BCD ; much more then is the ...
Página 17
... Spherical Trigonometry John Playfair. tion , as EG and FG ; then , upon the same base EF , and upon the same side of ... angle BAC coincides with the angle EDF , and is equal ( 8. Ax . ) to it . PROP . IX . PROB . To bisect a given ...
... Spherical Trigonometry John Playfair. tion , as EG and FG ; then , upon the same base EF , and upon the same side of ... angle BAC coincides with the angle EDF , and is equal ( 8. Ax . ) to it . PROP . IX . PROB . To bisect a given ...
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ABC is equal ABCD adjacent angles altitude angle ABC angle ACB angle BAC base BC bisected centre chord circle ABC circumference cosine cylinder demonstrated described diameter divided draw equal and similar equal angles equiangular equilateral equilateral polygon equimultiples Euclid exterior angle fore four right angles given rectilineal given straight line greater Hence hypotenuse inscribed join less Let ABC Let the straight magnitudes meet multiple opposite angle parallel parallelogram parallelopiped perpendicular polygon prism PROB PROP proportional proposition quadrilateral radius ratio rectangle contained rectilineal figure remaining angle right angled triangle SCHOLIUM segment semicircle shewn side BC sine solid angle solid parallelopiped spherical angle spherical triangle square straight line BC THEOR touches the circle triangle ABC triangle DEF wherefore