Elements of Geometry: Containing the First Six Books of Euclid, with Two Books on the Geometry of Solids. To which are Added, Elements of Plane and Spherical Trigonometry |
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Page iv
... enthusiastic . According- ly , he not only restored the text of EUCLID where- ever it had been corrupted , but in some cases removed imperfections that probably belonged to to the original work ; though his extreme par- tiality iv PREFACE .
... enthusiastic . According- ly , he not only restored the text of EUCLID where- ever it had been corrupted , but in some cases removed imperfections that probably belonged to to the original work ; though his extreme par- tiality iv PREFACE .
Page 14
... case in which the vertex of one triangle is upon a fide of the other , needs no demonstration . Therefore , upon the same base , and on the same side of it , there cannot be two triangles that have their fides which are terminated in ...
... case in which the vertex of one triangle is upon a fide of the other , needs no demonstration . Therefore , upon the same base , and on the same side of it , there cannot be two triangles that have their fides which are terminated in ...
Page 142
... B is not greater than A ; therefore A is equal to B. b A. 5 . Next , let C : A :: C : B , AB . For by inversion b , A : C :: B : C ; and therefore by the first case , A = B. PROP . : Book V. A F PROP . X. THE OR 142 ELEMENTS.
... B is not greater than A ; therefore A is equal to B. b A. 5 . Next , let C : A :: C : B , AB . For by inversion b , A : C :: B : C ; and therefore by the first case , A = B. PROP . : Book V. A F PROP . X. THE OR 142 ELEMENTS.
Page 150
... case , since C > A , F > D , that is , D < F . There- fore , & c . Q. E. D. I : PROP . XXII . THEOR . F there be any number of magnitudes , and as many others , which , taken two and two in order , have the fame ratio ; the first shall ...
... case , since C > A , F > D , that is , D < F . There- fore , & c . Q. E. D. I : PROP . XXII . THEOR . F there be any number of magnitudes , and as many others , which , taken two and two in order , have the fame ratio ; the first shall ...
Page 152
... case A : C :: E : G. But C : D :: G : H , therefore again , by the first cafe , A : D :: E : H. In the same manner may the demonstration be extended to any number of magnitudes . Therefore , & c . Q. E. D. a 22. 5 . b 18. 5 . I PROP ...
... case A : C :: E : G. But C : D :: G : H , therefore again , by the first cafe , A : D :: E : H. In the same manner may the demonstration be extended to any number of magnitudes . Therefore , & c . Q. E. D. a 22. 5 . b 18. 5 . I PROP ...
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Common terms and phrases
ABCD alfo alſo alſo equal angle ABC angle ACB angle BAC arch baſe baſe BC BC is equal becauſe becauſe the angle biſected Book VII caſe cauſe centre circle ABC circumference co-fine demonſtrated deſcribed diameter draw drawn equal angles equiangular equilateral equilateral polygon equimultiples Euclid exterior angle fame reaſon fides fimilar fince firſt folid fore given ſtraight line greater inſcribed interfect join leſs Let ABC line BC magnitudes oppoſite parallel parallelepiped parallelogram paſs paſſes perpendicular plane polygon priſm proportionals propoſition Q. E. D. PROP radius rectangle contained rectilineal figure remaining angle right angles ſame ſame manner ſame ratio ſecond ſection ſegment ſhall be equal ſhewn ſide ſolid ſpace ſpherical triangle ſquare of AC ſtand ſuch ſum ſuppoſed tangent THEOR theſe thoſe touches the circle triangle ABC wherefore
Popular passages
Page 19 - If two triangles have two angles of the one equal to two angles of the other, each to each, and one side equal to one side, viz. either the sides adjacent to the equal...
Page 155 - If two triangles have one angle of the one equal to one angle of the other and the sides about these equal angles proportional, the triangles are similar.
Page 17 - If, at a point in a straight line, two other straight lines upon the opposite sides of it, make the adjacent angles, together equal to two right angles, these two straight lines shall be in one and the same straight line.
Page 9 - Wherefore, from the given point A, a straight line AL has been drawn equal to the given straight line BC.
Page 3 - A circle is a plane figure contained by one line, which is called the circumference, and is such that all straight lines drawn from a certain point within the figure to the circumference, are equal to one another.
Page 23 - Therefore all the angles of the figure, together with four right angles, are equal to twice as many right angles as the figure has sides.
Page 12 - ABC: and it has also been proved that the angle FBC is equal to the angle GCB, which are the angles upon the other side of the base. Therefore the angles at the base, &c.
Page 6 - Let it be granted that a straight line may be drawn from any one point to any other point.
Page 156 - But by the hypothesis, it is less than a right angle ; which is absurd. Therefore the angles ABC, DEF are not unequal, that is, they are equal : And the angle at A is equal to the angle at D ; wherefore...
Page 44 - If a straight line be bisected, and produced to any point ; the rectangle contained by the whole line thus produced, and the part of it produced...