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 TrigonometryB. & S. Collins; W. E. Dean, printer, 1836 - 311 páginas |
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Página 22
... side AB lies in the same direction with DF , and AC in the same direction with DE , is necessary ; because the angle CAI would have its sides parallel to those of the angle EDF , but would not be equal to it . In that case , CAI and EDF ...
... side AB lies in the same direction with DF , and AC in the same direction with DE , is necessary ; because the angle CAI would have its sides parallel to those of the angle EDF , but would not be equal to it . In that case , CAI and EDF ...
Página 23
... sides , wanting four right angles . D For any rectilineal figure ABCDE can be divided into as many trian- gles as the figure has sides , by drawing straight lines from a point F within the figure to each of its angles . And , by the ...
... sides , wanting four right angles . D For any rectilineal figure ABCDE can be divided into as many trian- gles as the figure has sides , by drawing straight lines from a point F within the figure to each of its angles . And , by the ...
Página 24
... sides , wanting four . COR . 1. All the exterior angles of any rectilineal figure are together equal to four right angles . Because every interior an- gle ABC , with its adjacent exterior ABD , is equal ( 6. 1. ) to two right angles ...
... sides , wanting four . COR . 1. All the exterior angles of any rectilineal figure are together equal to four right angles . Because every interior an- gle ABC , with its adjacent exterior ABD , is equal ( 6. 1. ) to two right angles ...
Página 25
... sides AB , BC are equal to the two DC , CB ; and the angle ABC is equal to C B D the angle BCD ; therefore the base AC is equal ( 1. 1. ) to the base BD , and the triangle ABC to the triangle BCD , and the other angles to the other ...
... sides AB , BC are equal to the two DC , CB ; and the angle ABC is equal to C B D the angle BCD ; therefore the base AC is equal ( 1. 1. ) to the base BD , and the triangle ABC to the triangle BCD , and the other angles to the other ...
Página 26
... side BC , which is adjacent to these equal angles , common to the two triangles ; therefore their other sides are equal , each to each , and the third angle of the one to the third angle of the other ( Th . 2. ) ; viz . the side AB to the ...
... side BC , which is adjacent to these equal angles , common to the two triangles ; therefore their other sides are equal , each to each , and the third angle of the one to the third angle of the other ( Th . 2. ) ; viz . the side AB to the ...
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ABC is equal ABCD adjacent angles altitude angle ABC angle ACB angle BAC angles equal base BC bisected centre chord circle ABC circumference cosine cylinder demonstrated diameter divided equal and similar equal angles equiangular equilateral equilateral polygon equimultiples Euclid exterior angle fore four right angles 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 PROP 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 third touches the circle triangle ABC triangle DEF wherefore