The Elements of Euclid: Viz. the First Six Books, Together with the Eleventh and Twelfth |
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Page 30
... manner it may be de B D G monstrated , that they do not meet towards A , C : but those straight lines which meet neither way , * 35 De £ . though produced ever so far , are parallel * to one another : therefore AB is parallel to CD ...
... manner it may be de B D G monstrated , that they do not meet towards A , C : but those straight lines which meet neither way , * 35 De £ . though produced ever so far , are parallel * to one another : therefore AB is parallel to CD ...
Page 40
... manner , it can be demonstrated , that no other line but AD is parallel to BC ; AD is therefore parallel to it . Wherefore equal triangles upon , & c . Q. E. D. PROP . XL . THEOR . Equal triangles upon equal bases , in the same straight ...
... manner , it can be demonstrated , that no other line but AD is parallel to BC ; AD is therefore parallel to it . Wherefore equal triangles upon , & c . Q. E. D. PROP . XL . THEOR . Equal triangles upon equal bases , in the same straight ...
Page 41
... manner it can be demonstrated that there is no other parallel to it but AD : AD is therefore parallel to BF . Wherefore equal triangles , & c . Q. E. D. PROP . XLI . THEOR . If a parallelogram and a triangle be upon the same base , and ...
... manner it can be demonstrated that there is no other parallel to it but AD : AD is therefore parallel to BF . Wherefore equal triangles , & c . Q. E. D. PROP . XLI . THEOR . If a parallelogram and a triangle be upon the same base , and ...
Page 47
... manner , by joining AE , BK , it can be demonstrated , that the parallelogram CL is equal to the square HC : therefore the whole square BDEC is equal to the two squares GB , † 2 Ax . HC : and the square BDEC is described upon * 1 . 1 ...
... manner , by joining AE , BK , it can be demonstrated , that the parallelogram CL is equal to the square HC : therefore the whole square BDEC is equal to the two squares GB , † 2 Ax . HC : and the square BDEC is described upon * 1 . 1 ...
Page 50
... manner the rectangle EH is contained by A , EC : therefore the rectangle contained by A , BC , is equal to the several rectangles contained by A , BD , and by A , DE , and by A , EC . Wherefore , if there be two straight lines , & c ...
... manner the rectangle EH is contained by A , EC : therefore the rectangle contained by A , BC , is equal to the several rectangles contained by A , BD , and by A , DE , and by A , EC . Wherefore , if there be two straight lines , & c ...
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