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 57
... bisect it . Let ABC be a circle , and let CD , a straight line drawn through the cen- tre , bisect any straight line AB , which does not pass through the centre , in the point F ; It cuts it also at right angles . D Take E the centre of ...
... bisect it . Let ABC be a circle , and let CD , a straight line drawn through the cen- tre , bisect any straight line AB , which does not pass through the centre , in the point F ; It cuts it also at right angles . D Take E the centre of ...
Página 58
... bisect one another . A D For if it is possible , let AE be equal to EC , and BE to ED ; If one of the lines pass through the centre , it is plain that it cannot be bisected by the other , which does not pass through the centre . But if ...
... bisect one another . A D For if it is possible , let AE be equal to EC , and BE to ED ; If one of the lines pass through the centre , it is plain that it cannot be bisected by the other , which does not pass through the centre . But if ...
Página 61
... bisected by the perpendiculars DF , EF , which must meet in some point F ; for if they were parallel , the lines DB , CB , perpendicular to them would also be parallel ( Cor . 1. Th . 21. 1. ) , or else form but one straight line : but ...
... bisected by the perpendiculars DF , EF , which must meet in some point F ; for if they were parallel , the lines DB , CB , perpendicular to them would also be parallel ( Cor . 1. Th . 21. 1. ) , or else form but one straight line : but ...
Página 62
... bisecting the chord BC ( Cor . 1. Th . 3. 3. ) , must be at the intersection of these perpendiculars ; so that , as ... bisect the chord at right angles . COR . Hence , the line joining the intersections of the circumferences of two ...
... bisecting the chord BC ( Cor . 1. Th . 3. 3. ) , must be at the intersection of these perpendiculars ; so that , as ... bisect the chord at right angles . COR . Hence , the line joining the intersections of the circumferences of two ...
Página 65
... bisected , both the arc and the chord which it subtends shall also be bisected . COR . 4. It follows , likewise , that a perpendicular through the middle of the chord , bisects the angle at the centre , and passes through the middle of ...
... bisected , both the arc and the chord which it subtends shall also be bisected . COR . 4. It follows , likewise , that a perpendicular through the middle of the chord , bisects the angle at the centre , and passes through the middle of ...
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Términos y frases comunes
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