The Elements of Euclid: The Errors, by which Theon, Or Others, Have Long Ago Vitiated These Books, are Corrected and Some of Euclid's Demonstrations are Restored. Also, to this Second Edition is Added the Book of Euclid's Data. In Like Manner Corrected. viz. the first six books, together with the eleventh and twelfth |
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Page 3
... drawn from a cer- tain point within the figure to the circumference , are equal to one another . Book I. XVI . And this point is called the center of the circle . XVII . A diameter of a circle is a straight line drawn thro ' the center ...
... drawn from a cer- tain point within the figure to the circumference , are equal to one another . Book I. XVI . And this point is called the center of the circle . XVII . A diameter of a circle is a straight line drawn thro ' the center ...
Page 5
... drawn from any one point to any other point . II . That a terminated straight line may be produced to any length in a straight line . III . And that a circle may be described from any center , at any distance from that center . ΑΧΙOMS ...
... drawn from any one point to any other point . II . That a terminated straight line may be produced to any length in a straight line . III . And that a circle may be described from any center , at any distance from that center . ΑΧΙOMS ...
Page 14
... drawn from the given point C , is at right angles to the given straight line AB . Because DC is equal to CE , and FC common to the two tri- AD angles DCF , ECF ; the two fides C Ев DC , CF are equal to the two EC , CF , each to each ...
... drawn from the given point C , is at right angles to the given straight line AB . Because DC is equal to CE , and FC common to the two tri- AD angles DCF , ECF ; the two fides C Ев DC , CF are equal to the two EC , CF , each to each ...
Page 15
... drawn from the given point C , is per- pendicular to the given straight line AB . e 1 . Because FH is equal to HG , and HC common to the two triangles FHC , GHC , the two fides FH , HC are equal to the two GH , HC , each to each ; and ...
... drawn from the given point C , is per- pendicular to the given straight line AB . e 1 . Because FH is equal to HG , and HC common to the two triangles FHC , GHC , the two fides FH , HC are equal to the two GH , HC , each to each ; and ...
Page 20
... drawn two ftraight lines to a point within the triangle , these shall be less than the other two sides of the triangle , but shall contain a greater angle . Let the two straight lines BD , CD be drawn from B , C , the ends of the side ...
... drawn two ftraight lines to a point within the triangle , these shall be less than the other two sides of the triangle , but shall contain a greater angle . Let the two straight lines BD , CD be drawn from B , C , the ends of the side ...
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Common terms and phrases
alfo alſo angle ABC angle BAC bafe baſe BC is equal BC is given becauſe the angle becauſe the ratio biſected Book XI cafe cauſe circle ABCD circumference cone conſtruction cylinder demonftrated deſcribed diameter drawn equal angles equiangular equimultiples Euclid exceſs fame multiple fame ratio fame reaſon fides fimilar firſt folid angle 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 likewife oppoſite parallel parallelepipeds parallelogram perpendicular priſms Propofition proportionals pyramid Q. E. D. PROP rectangle rectangle contained rectilineal figure right angles ſame ſecond ſegment ſhall ſhewn ſide ſpace ſphere ſquare of AC ſtraight line AB ſtraight line BC THEOR theſe thoſe tiple triangle ABC vertex wherefore
Popular passages
Page 5 - Let it be granted that a straight line may be drawn from any one point to any other point.
Page 163 - 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 48 - If a straight line be divided into any two parts, the squares of the whole line, and of one of the parts, are equal to twice the rectangle contained by the whole and that part, together with the square of the other part. Let the straight line AB be divided into any two parts in the point C; the squares of AB, BC are equal to twice the rectangle AB, BC, together with the square of AC.
Page 73 - The straight line drawn at right angles to the diameter of a circle, from the extremity of it, falls without the circle; and no straight line can be drawn from the extremity between that straight line and the circumference, so as not to cut the circle...
Page 105 - 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 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 167 - Similar triangles are to one another in the duplicate ratio of their homologous sides.
Page 54 - AB be the given straight line ; it is required to divide it into two parts, so that the rectangle contained by the whole, and one of the parts, shall be equal to the square of the other part.
Page 47 - If a straight line be divided into two equal parts, and also into two unequal parts; the rectangle contained by the unequal parts, together with the square of the line between the points of section, is equal to the square of half the line.
Page 37 - To describe a parallelogram that shall be equal to a given triangle, and have one of its angles equal to a given rectilineal angle.