The Elements of Euclid |
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Page viii
... likewise is of the greatest use in the arts both of peace and war , to many of which geometry is absolute- ly necessary . This I have endeavoured to do , by taking away the inaccurate and false reasonings which unskilful editors have ...
... likewise is of the greatest use in the arts both of peace and war , to many of which geometry is absolute- ly necessary . This I have endeavoured to do , by taking away the inaccurate and false reasonings which unskilful editors have ...
Page 16
... likewise equal to AD ; whence AE and C are each of them equal to AD ; wherefore the straight line AE is equal to e C , and from AB , the greater of two straight lines , a part AE has been cut off equal to C the less . Which was to be ...
... likewise equal to AD ; whence AE and C are each of them equal to AD ; wherefore the straight line AE is equal to e C , and from AB , the greater of two straight lines , a part AE has been cut off equal to C the less . Which was to be ...
Page 17
... likewise the angles contained by those sides equal to one another , their bases shall likewise be equal , and the triangles be equal , and their other angles to which the equal sides are opposite shall be equal , each to each . Which ...
... likewise the angles contained by those sides equal to one another , their bases shall likewise be equal , and the triangles be equal , and their other angles to which the equal sides are opposite shall be equal , each to each . Which ...
Page 19
... likewise those which are terminated in the other extremity . If it be possible , let there be two triangles ACB , ADB , up- on the same base AB , and upon the same side of it , which have their sides CA , DA , terminated in the ...
... likewise those which are terminated in the other extremity . If it be possible , let there be two triangles ACB , ADB , up- on the same base AB , and upon the same side of it , which have their sides CA , DA , terminated in the ...
Page 20
... likewise greater than BCD ; much more than is the angle BDC greater then the angle BCD . Again , because CB is equal to DB , the angle BDC is equal to the angle BCD ; but BDC has been proved A . to be greater than the same BCD ; which ...
... likewise greater than BCD ; much more than is the angle BDC greater then the angle BCD . Again , because CB is equal to DB , the angle BDC is equal to the angle BCD ; but BDC has been proved A . to be greater than the same BCD ; which ...
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Common terms and phrases
altitude angle ABC angle BAC base BC BC is equal BC is given bisected Book XI centre circle ABCD circumference cone cylinder demonstrated described diameter draw drawn equal angles equiangular equimultiples Euclid excess fore given angle given in magnitude given in position given in species given magnitude given ratio given straight line gnomon greater join less Let ABC meet multiple parallel parallelogram parallelogram AC perpendicular point F polygon prism proportionals proposition pyramid Q. E. D. PROP radius ratio of AE rectangle CB rectangle contained rectilineal figure remaining angle right angles segment sides BA similar solid angle solid parallelopiped square of AC straight line AB straight line BC tangent THEOR third triangle ABC triplicate ratio vertex wherefore