The Elements of Euclid |
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Page 13
... described from any centre , at any dis- tance from that centre . AXIOMS . I. THINGS which are equal to the same are equal to one another . II . If equals be added to equals , the wholes are equal . III . IV . If equals be taken from ...
... described from any centre , at any dis- tance from that centre . AXIOMS . I. THINGS which are equal to the same are equal to one another . II . If equals be added to equals , the wholes are equal . III . IV . If equals be taken from ...
Page 15
... described upon the given straight line AB . Which was required to be done . PROP . II . PROB . FROM a given point to ... described the circle CGH , and from the centre D , at the distance DG , describe the cir- cle GKL . AL shall be ...
... described upon the given straight line AB . Which was required to be done . PROP . II . PROB . FROM a given point to ... described the circle CGH , and from the centre D , at the distance DG , describe the cir- cle GKL . AL shall be ...
Page 44
... the parallelogram FECG is equal to the triangle ABC , and it has one of its angles CEF equal to the given angle D. Wherefore there has been described a parallelogram B E C FECG equal to a given triangle ABC , having one THE ELEMENTS.
... the parallelogram FECG is equal to the triangle ABC , and it has one of its angles CEF equal to the given angle D. Wherefore there has been described a parallelogram B E C FECG equal to a given triangle ABC , having one THE ELEMENTS.
Page 47
... described equal to the given rec- tilineal figure ABCD , having the angle FKM equal to the gi ven angle E. Which was to be done . e COR . From this it is manifest how to a given straight line to apply a parallelogram , which shall have ...
... described equal to the given rec- tilineal figure ABCD , having the angle FKM equal to the gi ven angle E. Which was to be done . e COR . From this it is manifest how to a given straight line to apply a parallelogram , which shall have ...
Page 48
... described upon the sides which contain the right angle . Let ABC be a right angled triangle , having the right angle . BAC ; the square described upon the side BC is equal to the squares described upon BA , AC . On BC describe the ...
... described upon the sides which contain the right angle . Let ABC be a right angled triangle , having the right angle . BAC ; the square described upon the side BC is equal to the squares described upon BA , AC . On BC describe the ...
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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