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 8
... angle is the inclination of two straight lines to one another , which meet together , but are not in the same ... ABC , or CBA ; that which is contained by AB , The definitions marked with inverted commas are different from those of Euclid .
... angle is the inclination of two straight lines to one another , which meet together , but are not in the same ... ABC , or CBA ; that which is contained by AB , The definitions marked with inverted commas are different from those of Euclid .
Página 13
... angle ABC to the triangle DEF ; and the other an- gles , to which the equal sides are opposite , shall be equal , each to each , AA B E F viz . the angle ABC to the angle DEF , and the angle ACB to DFE . For , if the triangle ABC be ...
... angle ABC to the triangle DEF ; and the other an- gles , to which the equal sides are opposite , shall be equal , each to each , AA B E F viz . the angle ABC to the angle DEF , and the angle ACB to DFE . For , if the triangle ABC be ...
Página 14
... angle BAC is equal to the angle EDF ; wherefore also the point C shall ... ABC shall coincide with the whole triangle DEF , so that the spaces which ... angle ABC to the angle DEF , and the angle ACB to the angle DFE . Therefore , if two ...
... angle BAC is equal to the angle EDF ; wherefore also the point C shall ... ABC shall coincide with the whole triangle DEF , so that the spaces which ... angle ABC to the angle DEF , and the angle ACB to the angle DFE . Therefore , if two ...
Página 15
... 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 triangle is also equiangular PROP . VI . THEOR . If two ...
... 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 triangle is also equiangular PROP . VI . THEOR . If two ...
Página 16
... angle which is contain ed by the two sides of the one shall be equal to the angle contained by the two sides of the other . Let ABC , DEF be two triangles having the two sides AB , AC , equal to the two sides DE , DF , each to each ...
... angle which is contain ed by the two sides of the one shall be equal to the angle contained by the two sides of the other . Let ABC , DEF be two triangles having the two sides AB , AC , equal to the two sides DE , DF , each to each ...
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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