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 15
... shewn that it is not equal to AB ; therefore AC is greater than AB . PROP . XIII . THEOR . Any two sides of a triangle are together greater than the third side . Let ABC be a triangle ; any two sides of it together are greater than the ...
... shewn that it is not equal to AB ; therefore AC is greater than AB . PROP . XIII . THEOR . Any two sides of a triangle are together greater than the third side . Let ABC be a triangle ; any two sides of it together are greater than the ...
Página 16
... shewn that BA , AC are greater than BE , EC ; much more then are BA , AC greater than BD , DC . D A. E Again , because the exterior angle of a triangle ( 9. 1. ) is greater than the interior and opposite angle , the exterior angle BDC ...
... shewn that BA , AC are greater than BE , EC ; much more then are BA , AC greater than BD , DC . D A. E Again , because the exterior angle of a triangle ( 9. 1. ) is greater than the interior and opposite angle , the exterior angle BDC ...
Página 17
... ; therefore the angle BAC is not less than the angle EDF and it was shewn that it is not equal to it : therefore the angle BAC is greater than the angle EDF . PROP . XVII . THEOR . A perpendicular is the 3 OF GEOMETRY . BOOK I. 17.
... ; therefore the angle BAC is not less than the angle EDF and it was shewn that it is not equal to it : therefore the angle BAC is greater than the angle EDF . PROP . XVII . THEOR . A perpendicular is the 3 OF GEOMETRY . BOOK I. 17.
Página 22
... shewn that the angle AGK is equal to the angle GHF ; therefore also AGK is equal to GKD ; and they are alternate angles ; therefore AB is pa- rallel ( 19. 1. ) to CD . F A G B E H K D PROP . XXIV . THEOR . Two angles are equal if their ...
... shewn that the angle AGK is equal to the angle GHF ; therefore also AGK is equal to GKD ; and they are alternate angles ; therefore AB is pa- rallel ( 19. 1. ) to CD . F A G B E H K D PROP . XXIV . THEOR . Two angles are equal if their ...
Página 23
... shewn to be equal to the angle BAC ; therefore the whole ex- terior angle ACD is equal to the two interior and opposite angles CAB , ABC ; to these angles add the angle ACB , and the angles ACD , ACB are equal to the three angles CBA ...
... shewn to be equal to the angle BAC ; therefore the whole ex- terior angle ACD is equal to the two interior and opposite angles CAB , ABC ; to these angles add the angle ACB , and the angles ACD , ACB are equal to the three angles CBA ...
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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