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 14
... remaining angles of the one shall coincide with the remaining angles of the other , and be equal to them , viz . the angle ABC to the angle DEF , and the angle ACB to the angle DFE . Therefore , if two triangles have two sides of the ...
... remaining angles of the one shall coincide with the remaining angles of the other , and be equal to them , viz . the angle ABC to the angle DEF , and the angle ACB to the angle DFE . Therefore , if two triangles have two sides of the ...
Página 20
... angles ; but the angles ABC , ABD are likewise together equal to two right angles : therefore the angles CBA , ABE are equal to the angles CBA , ABD : Take away the common angle ABC , and the remaining angle ABE is equal ( 3. Ax . ) to the ...
... angles ; but the angles ABC , ABD are likewise together equal to two right angles : therefore the angles CBA , ABE are equal to the angles CBA , ABD : Take away the common angle ABC , and the remaining angle ABE is equal ( 3. Ax . ) to the ...
Página 21
... remaining angles to the remaining angles each to each , to which the equal sides are oppo- site ; wherefore the angle BAE is equal to the angle ECF ; but the angle ECD is greater than the an- gle ECF ; therefore the angle ECD , that is ...
... remaining angles to the remaining angles each to each , to which the equal sides are oppo- site ; wherefore the angle BAE is equal to the angle ECF ; but the angle ECD is greater than the an- gle ECF ; therefore the angle ECD , that is ...
Página 28
... angles , the angles AGH , BGH are equal to the angles BGH , GHD : Take away the common angle BGH ; therefore the remaining angle AGH is equal to the remaining angle GHD ; and they are alternate angles ; therefore AB is parallel to CD ...
... angles , the angles AGH , BGH are equal to the angles BGH , GHD : Take away the common angle BGH ; therefore the remaining angle AGH is equal to the remaining angle GHD ; and they are alternate angles ; therefore AB is parallel to CD ...
Página 32
... angles ; that is , as many times two right an- gles as there are units in the ... angle ABC is equal to C B D the angle BCD ; therefore the base AC is equal ... remaining sides will also be equal and parallel , and the figure will be a ...
... angles ; that is , as many times two right an- gles as there are units in the ... angle ABC is equal to C B D the angle BCD ; therefore the base AC is equal ... remaining sides will also be equal and parallel , and the figure will be a ...
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Términos y frases comunes
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