The Elements of Euclid: Viz. the First Six Books, Together with the Eleventh and Twelfth |
From inside the book
Page 11
... angles of the one coincide with the remaining angles of the other , and are equal to them , viz . the angle ABC to the angle DEF , and the angle ACB to DFE . Therefore , if two triangles have two sides of the one equal to two sides of ...
... angles of the one coincide with the remaining angles of the other , and are equal to them , viz . the angle ABC to the angle DEF , and the angle ACB to DFE . Therefore , if two triangles have two sides of the one equal to two sides of ...
Page 12
... angle BFC was proved to be equal to the angle CGB , and the base BC is common to the two triangles BFC , CGB ; wherefore these triangles are equal * , and their remaining angles each to each , to which the equal sides are opposite ...
... angle BFC was proved to be equal to the angle CGB , and the base BC is common to the two triangles BFC , CGB ; wherefore these triangles are equal * , and their remaining angles each to each , to which the equal sides are opposite ...
Page 20
... remaining angle ABE is equal to the remaining angle ABD , the less to the greater , which is impossible ; therefore BE is not in the same straight line with BC . And in like manner , it may be demonstrated that no other can be in the ...
... remaining angle ABE is equal to the remaining angle ABD , the less to the greater , which is impossible ; therefore BE is not in the same straight line with BC . And in like manner , it may be demonstrated that no other can be in the ...
Page 21
... angle is greater than either of the interior op- posite angles .. Let ABC be a triangle , and let its side BC be ... remaining , angles to the reinairing angles , each to each , to which the equal sides are oppo- site : wherefore the angle ...
... angle is greater than either of the interior op- posite angles .. Let ABC be a triangle , and let its side BC be ... remaining , angles to the reinairing angles , each to each , to which the equal sides are oppo- site : wherefore the angle ...
Page 31
... angle EGB equal to the interior and opposite angle GHD upon the same side ; or make the interior angles on the same ... remaining angle AGH is equal to the † 3 Ax . remaining angle GHD : and they are alternate angles : therefore ABis ...
... angle EGB equal to the interior and opposite angle GHD upon the same side ; or make the interior angles on the same ... remaining angle AGH is equal to the † 3 Ax . remaining angle GHD : and they are alternate angles : therefore ABis ...
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