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 TrigonometryE. Duyckinck, and George Long, 1824 - 333 páginas |
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Página 25
... fore , if two angles , & c . Q. E. D. B COR . Hence every equiangular triangle is also equilateral . PROP . VII . THEOR . Upon the same base , and on the same side of it , there cannot be two tri- angles , that have their sides which ...
... fore , if two angles , & c . Q. E. D. B COR . Hence every equiangular triangle is also equilateral . PROP . VII . THEOR . Upon the same base , and on the same side of it , there cannot be two tri- angles , that have their sides which ...
Página 26
... fore the angle ADC is greater also than BCD ; much more then is the angle BDC greater than the angle : A B BCD . Again , because CB is equal to DB , the angle BDC is equal ( 5. 1. ) to the angle BCD ; but it has been demonstrated to be ...
... fore the angle ADC is greater also than BCD ; much more then is the angle BDC greater than the angle : A B BCD . Again , because CB is equal to DB , the angle BDC is equal ( 5. 1. ) to the angle BCD ; but it has been demonstrated to be ...
Página 27
... angle DAF is equal ( 8.1 . ) to the angle EAF : where- fore the given rectilineal angle BAC is bisected by the straight line AF . Which was to be done . A F B E PROP . X. PROB . To bisect a given finite OF GEOMETRY . BOOK I. 27 A ...
... angle DAF is equal ( 8.1 . ) to the angle EAF : where- fore the given rectilineal angle BAC is bisected by the straight line AF . Which was to be done . A F B E PROP . X. PROB . To bisect a given finite OF GEOMETRY . BOOK I. 27 A ...
Página 31
... fore , if two straight lines , & c . Q. E. D. COR . 1. From this it is manifest , that if two straight lines cut one another , the angles which they make at the point of their intersec- tion , are together equal to four right angles ...
... fore , if two straight lines , & c . Q. E. D. COR . 1. From this it is manifest , that if two straight lines cut one another , the angles which they make at the point of their intersec- tion , are together equal to four right angles ...
Página 35
... fore , also GK is equal to C ; and FG is equal to B ; therefore the three straight lines KF , FG , GK , are equal to the three A , B , C : And therefore the triangle KFG has its three sides KF , FG , GK equal to the three given straight ...
... fore , also GK is equal to C ; and FG is equal to B ; therefore the three straight lines KF , FG , GK , are equal to the three A , B , C : And therefore the triangle KFG has its three sides KF , FG , GK equal to the three given straight ...
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ABC is equal ABCD altitude angle ABC angle ACB angle BAC angle EDF arch AC base BC bisected centre circle ABC circumference cosine cylinder demonstrated diameter draw equal angles equiangular equilateral equilateral polygon equimultiples Euclid exterior angle fore four right angles given straight line greater hypotenuse inscribed join less Let ABC Let the straight line BC magnitudes meet multiple opposite angle parallel parallelepipeds parallelogram perpendicular polygon prism PROB produced proportionals proposition Q. E. D. COR Q. E. D. PROP radius ratio rectangle contained rectilineal figure remaining angle segment semicircle shewn side BC sine solid angle solid parallelepipeds spherical angle spherical triangle straight line AC THEOR third touches the circle triangle ABC triangle DEF wherefore