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 1
... extremities of a line are points ; and " the intersections of one line with another are also points . " III . " Lines which cannot coincide in two points , without coin- ciding altogether , are called straight lines . 66 " COR . Hence ...
... extremities of a line are points ; and " the intersections of one line with another are also points . " III . " Lines which cannot coincide in two points , without coin- ciding altogether , are called straight lines . 66 " COR . Hence ...
Page 13
... extremity of the bafe equal to one another , and likewife those which are terminated in the other extremity , equal to one another . If it be poffible , let there be two triangles ACB , ADB , upon the fame base AB , and upon the fame ...
... extremity of the bafe equal to one another , and likewife those which are terminated in the other extremity , equal to one another . If it be poffible , let there be two triangles ACB , ADB , upon the fame base AB , and upon the fame ...
Page 14
... extremity of the base equal to one another , and likewise those which are terminated in the other extre- mity . Q. E. D. It PROP . VIII . THEOR F two triangles have two fides of the one equal to two fides of the other , each to each ...
... extremity of the base equal to one another , and likewise those which are terminated in the other extre- mity . Q. E. D. It PROP . VIII . THEOR F two triangles have two fides of the one equal to two fides of the other , each to each ...
Page 15
... extremity of the base equal to one Book I. another , and likewife their fides terminated in the other extremity : But this is impoffible ; therefore , if the bafe BC coincides with the base EF , the fides BA , AC cannot but coincide ...
... extremity of the base equal to one Book I. another , and likewife their fides terminated in the other extremity : But this is impoffible ; therefore , if the bafe BC coincides with the base EF , the fides BA , AC cannot but coincide ...
Page 17
... extremity of the base equal to one another , and likewise those which are terminated in the other extre- mity . Q. E. D. If two PROP . VIII . THE OR 9 % 79. 16 . f F two triangles have two fides of the one equal to two fides of the ...
... extremity of the base equal to one another , and likewise those which are terminated in the other extre- mity . Q. E. D. If two PROP . VIII . THE OR 9 % 79. 16 . f F two triangles have two fides of the one equal to two fides of the ...
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Common terms and phrases
ABCD adjacent angles alfo alfo equal alſo angle ABC angle ACB angle BAC arch bafe baſe BC is equal becauſe the angle bifected Book VII cafe centre circle ABC circumference co-fine defcribed demonftrated diameter draw drawn equal angles equiangular equilateral equilateral polygon equimultiples Euclid exterior angle faid fame manner fame ratio fame reaſon fecond fection fegment femicircle fhewn fimilar fince firft firſt folid fore fquare of AC ftraight line AB fuch given ſtraight line greater impoffible infcribed interfection join lefs leſs Let ABC line BC magnitudes muſt oppofite angle parallel parallelepiped parallelogram perpendicular polygon prifm propofition proportionals radius rectangle contained rectilineal figure remaining angle right angles ſpace ſpherical triangle ſquare tangent thefe THEOR theſe thoſe touches the circle triangle ABC wherefore
Popular passages
Page 18 - 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...