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 TrigonometryJ.B. Lippincott, 1857 - 317 σελίδες |
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Σελίδα 18
... base DF is also equal to the base EF ; therefore the angle DCF is equal ( 8. 1. ) to the angle ECF ; and they are adjacent an- gles . But , when the adjacent angles which one straight line makes with another straight line are equal to ...
... base DF is also equal to the base EF ; therefore the angle DCF is equal ( 8. 1. ) to the angle ECF ; and they are adjacent an- gles . But , when the adjacent angles which one straight line makes with another straight line are equal to ...
Σελίδα 20
... AE is equal to EC , and BE to EF ; AE , EB are equal to CE , EF , each to each ; and the angle AEB is equal ( 15. 1. ) to the angle CEF , because they are vertical angles ; therefore the base AB is equal ( 4. 1 ) to the base CF 20 ELEMENTS.
... AE is equal to EC , and BE to EF ; AE , EB are equal to CE , EF , each to each ; and the angle AEB is equal ( 15. 1. ) to the angle CEF , because they are vertical angles ; therefore the base AB is equal ( 4. 1 ) to the base CF 20 ELEMENTS.
Σελίδα 24
... base DE to the base FG ; the angle DCE is equal ( 8. 1. ) to the angle FAG . C. A G E F D B Therefore , at the given point A in the given straight line AB , the angle FAG is made equal to the given rectilineal angle DCE . PROP . XXIV ...
... base DE to the base FG ; the angle DCE is equal ( 8. 1. ) to the angle FAG . C. A G E F D B Therefore , at the given point A in the given straight line AB , the angle FAG is made equal to the given rectilineal angle DCE . PROP . XXIV ...
Σελίδα 25
... base BC is also greater than the base EF . Of the two sides DE , DF , let DE be the side which is not greater than the other , and at the point D , in the straight line DE , make ( 23. 1. ) the angle EDG equal to the angle BAC : and ...
... base BC is also greater than the base EF . Of the two sides DE , DF , let DE be the side which is not greater than the other , and at the point D , in the straight line DE , make ( 23. 1. ) the angle EDG equal to the angle BAC : and ...
Σελίδα 26
... base GC is equal ( 4. 1. ) to the base DF , and the triangle GBC to the triangle DEF , and the other angles to the other angles , each to each , to which the equal sides are opposite ; therefore the angle GCB is equal to the angle DFE ...
... base GC is equal ( 4. 1. ) to the base DF , and the triangle GBC to the triangle DEF , and the other angles to the other angles , each to each , to which the equal sides are opposite ; therefore the angle GCB is equal to the angle DFE ...
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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 magnitudes meet multiple opposite angle parallel parallelogram parallelopiped perpendicular plane 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 third touches the circle triangle ABC triangle DEF wherefore