The Elements of Euclid |
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Page v
... adding some things , suppressing others , and mixing his own with Euclid's demonstrations , had chang ed more things to the worse than is commonly supposed , and those not of small moment , especially in the fifth and cleventh books of ...
... adding some things , suppressing others , and mixing his own with Euclid's demonstrations , had chang ed more things to the worse than is commonly supposed , and those not of small moment , especially in the fifth and cleventh books of ...
Page viii
... added at the end of the sixth book . Also the note on the 29th prop . book 1st , is altered , and made more explicit , and a more general demon- stration is given , instead of that which was in the note on the 10th definition of book ...
... added at the end of the sixth book . Also the note on the 29th prop . book 1st , is altered , and made more explicit , and a more general demon- stration is given , instead of that which was in the note on the 10th definition of book ...
Page 13
... added to equals , the wholes are equal . III . IV . If equals be taken from equals , the remainders are equal . 1 If equals be added to unequals , the wholes are unequal . V. If equals be taken from unequals , the remainders are unequal ...
... added to equals , the wholes are equal . III . IV . If equals be taken from equals , the remainders are equal . 1 If equals be added to unequals , the wholes are unequal . V. If equals be taken from unequals , the remainders are unequal ...
Page 58
... the square of AC , is equal to the square of AD , that is , of AB and BC added together in one straight line . Wherefore , if a straight line , & c . Q. E. D. ith W. 2 day PROP . IX . THEOR . Book II . IF 58 THE ELEMENTS.
... the square of AC , is equal to the square of AD , that is , of AB and BC added together in one straight line . Wherefore , if a straight line , & c . Q. E. D. ith W. 2 day PROP . IX . THEOR . Book II . IF 58 THE ELEMENTS.
Page 112
... added BCD , the whole ABCD is equal to the whole EDCB and the angle AED stands on the circumference ABCD , and the angle BAE on the circumference EDCB ; therefore the angle BAE is equal to the angle AED : for the same reason , each of ...
... added BCD , the whole ABCD is equal to the whole EDCB and the angle AED stands on the circumference ABCD , and the angle BAE on the circumference EDCB ; therefore the angle BAE is equal to the angle AED : for the same reason , each of ...
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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