The Elements of Euclid |
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Page 23
... perpendicular to a given straight line of an unlimited length , from a given ) point without it . zi Let AB be the given straight line , which may be produced to any length both ways , and let C be a point without it . It is re- quired ...
... perpendicular to a given straight line of an unlimited length , from a given ) point without it . zi Let AB be the given straight line , which may be produced to any length both ways , and let C be a point without it . It is re- quired ...
Page 63
... perpendicular falls , and the straight line intercepted without the triangle between the perpendicular and the obtuse angle . Book II . Let ABC be an obtuse angled triangle , having the obtuse angle ACB , and from the point A let AD be ...
... perpendicular falls , and the straight line intercepted without the triangle between the perpendicular and the obtuse angle . Book II . Let ABC be an obtuse angled triangle , having the obtuse angle ACB , and from the point A let AD be ...
Page 64
... perpendicular let fall up- on it from the opposite angle , and the acute angle . Let ABC be any triangle , and the angle at B one of its acute angles , and upon BC , one of the sides containing it , let fall the perpendiculara AD from ...
... perpendicular let fall up- on it from the opposite angle , and the acute angle . Let ABC be any triangle , and the angle at B one of its acute angles , and upon BC , one of the sides containing it , let fall the perpendiculara AD from ...
Page 65
... perpendicular to BC ; then is BC the straight line between the perpendicular and the acute angle at B ; and it is manifest that the square of AB , BC are equal to the square of AC and twice the square of BC . Therefore , in every ...
... perpendicular to BC ; then is BC the straight line between the perpendicular and the acute angle at B ; and it is manifest that the square of AB , BC are equal to the square of AC and twice the square of BC . Therefore , in every ...
Page 67
... a circle , when the perpendiculars drawn to them from the centre are equal . V. And the straight line on which the greater perpendicular falls , is said to be farther from the centre . Book III . VI . segment of a circle is THE ...
... a circle , when the perpendiculars drawn to them from the centre are equal . V. And the straight line on which the greater perpendicular falls , is said to be farther from the centre . Book III . VI . segment of a circle is 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