The Elements of Euclid: Viz. the First Six Books, Together with the Eleventh and Twelfth |
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Page 23
... shown that it is not equal to AB ; there- fore AC is greater than AB . greater angle , & c . Q. E. D. Wherefore the PROP . XX . THEOR . Any two sides of a triangle are together greater than the third side . Let ABC be a triangle : any ...
... shown that it is not equal to AB ; there- fore AC is greater than AB . greater angle , & c . Q. E. D. Wherefore the PROP . XX . THEOR . Any two sides of a triangle are together greater than the third side . Let ABC be a triangle : any ...
Page 24
... shown that BA , AC are greater than BE , EC ; much more then are BA , AC , greater than BD , DC . Again , because the exterior angle of a triangle * is greater than the interior and opposite angle , the exterior angle BDC of the ...
... shown that BA , AC are greater than BE , EC ; much more then are BA , AC , greater than BD , DC . Again , because the exterior angle of a triangle * is greater than the interior and opposite angle , the exterior angle BDC of the ...
Page 28
... shown that it is not equal to it ; therefore the angle BAC is greater than the angle EDF . Wherefore , if two triangles , & c . Q. E. D. +3.1 . + Hyp . PROP . XXVI . THEOR . If two triangles have two angles of the one equal to two ...
... shown that it is not equal to it ; therefore the angle BAC is greater than the angle EDF . Wherefore , if two triangles , & c . Q. E. D. +3.1 . + Hyp . PROP . XXVI . THEOR . If two triangles have two angles of the one equal to two ...
Page 32
... cuts the parallel straight lines EF , CD , the E * 29 . 1. angle GHF is equal * to the C- angle GKD and it was shown that the angle AGK -B H -F -D is equal to the angle GHF ; therefore also AGK 32 EUCLID'S ELEMENTS .
... cuts the parallel straight lines EF , CD , the E * 29 . 1. angle GHF is equal * to the C- angle GKD and it was shown that the angle AGK -B H -F -D is equal to the angle GHF ; therefore also AGK 32 EUCLID'S ELEMENTS .
Page 34
... shown to be equal to the angle BAC ; therefore the whole +2 Ax .. exterior angle ACD is equal † to the two interior and opposite angles CAB , ABC : to each of these equals add the angle ACB , and the angles ACD , +2 Ax . ACB are equal ...
... shown to be equal to the angle BAC ; therefore the whole +2 Ax .. exterior angle ACD is equal † to the two interior and opposite angles CAB , ABC : to each of these equals add the angle ACB , and the angles ACD , +2 Ax . ACB are equal ...
Other editions - View all
The Elements of Euclid: Viz. the First Six Books, Together with the Eleventh ... Euclid No preview available - 2015 |
The Elements of Euclid: Viz. the First Six Books, Together With the Eleventh ... Euclid No preview available - 2023 |
Common terms and phrases
AB is equal altitude angle ABC angle ACB angle BAC angle EDF base BC base DEF BC is equal bisected centre circle ABCD circle EFGH circumference cone Const cylinder described diameter draw equal angles equal to AC equiangular equilateral equimultiples exterior angle fore given rectilineal given straight line gnomon inscribed join less Let ABC multiple parallel parallelogram perpendicular point F polygon prism PROB pyramid ABCG pyramid DEFH Q. E. D. PROP rectangle contained rectilineal figure remaining angle right angles segment solid angle solid CD solid parallelopiped sphere square of AC straight line AB straight line AC THEOR three plane angles tiple touches the circle triangle ABC triangle DEF triplicate ratio wherefore whole