The Elements of Euclid; viz. the first six books,together with the eleventh and twelfth, with an appendix |
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Page 127
... equimultiples whatsoever of the first and third being taken , and any equimultiples whatsoever of the second and fourth ; if the multiple of the first be less than that of the second , the multiple of the third is also less than that of ...
... equimultiples whatsoever of the first and third being taken , and any equimultiples whatsoever of the second and fourth ; if the multiple of the first be less than that of the second , the multiple of the third is also less than that of ...
Page 131
... EQUIMULTIPLES of the same , or of equal magnitudes , are equal to one another.a II . Those magnitudes , of which the same or equal magni- tudes are equimultiples , are equal to one another . III . A multiple of a greater magnitude is ...
... EQUIMULTIPLES of the same , or of equal magnitudes , are equal to one another.a II . Those magnitudes , of which the same or equal magni- tudes are equimultiples , are equal to one another . III . A multiple of a greater magnitude is ...
Page 132
... equimultiples of as many , each of each ; what multiple soever any one of them is of its part , the same multiple shall all the first magnitudes be of all the other ; ' For ' the same demonstration holds in any number of mag- ' nitudes ...
... equimultiples of as many , each of each ; what multiple soever any one of them is of its part , the same multiple shall all the first magnitudes be of all the other ; ' For ' the same demonstration holds in any number of mag- ' nitudes ...
Page 133
... equimultiples , these shall be equimultiples , the one of the second , and the other of the fourth . Let A the first be the same multiple of B the se- cond , that C the third is of D the fourth ; and of A , C let the equimultiples EF ...
... equimultiples , these shall be equimultiples , the one of the second , and the other of the fourth . Let A the first be the same multiple of B the se- cond , that C the third is of D the fourth ; and of A , C let the equimultiples EF ...
Page 134
... equimultiples whatever of the first and third shall have the same ratio to any equimultiples of the second and fourth , viz . ' the equimultiple of the first shall have the same ratio to that of the second , which the equimultiple of ...
... equimultiples whatever of the first and third shall have the same ratio to any equimultiples of the second and fourth , viz . ' the equimultiple of the first shall have the same ratio to that of the second , which the equimultiple of ...
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The Elements of Euclid: Viz. the First Six Books, Together with the Eleventh ... Euclid No preview available - 2015 |
Common terms and phrases
AB is equal AC is equal altitude angle ABC angle ACB angle BAC base BC bisect centre circle ABCD circle EFGH circumference common section cone cylinder demonstrated described diameter draw equal to F equiangular equilateral equimultiples exterior angle fore given rectilineal given straight line gnomon inscribed join less Let ABC meet multiple opposite angle parallel parallelogram parallelopiped perpendicular polygon prisms PROB proved pyramid ABCG pyramid DEFH Q. E. D. PROP rectangle contained rectilineal figure remaining angle right angles segment solid angle solid CD sphere square of AC straight line AC THEOR third three plane angles three straight lines tiples touches the circle triangle ABC triangle DEF triplicate ratio twice the rectangle wherefore whole
Popular passages
Page 173 - 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 56 - Iff a straight line be divided into any two parts, four times the rectangle contained by the whole line, and one of the parts, together with the square of the other part, is equal to the square of the straight line which is made up of the whole and that part.
Page 53 - 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 on the line between the points of section, is equal to the square on half the line.
Page 58 - IF a straight line be divided into two equal, and also into two unequal parts; the squares of the two unequal parts are together double of the square of half the line, and of the square of the line between the points of section.
Page 94 - The angle in a semicircle is a right angle ; the angle in a segment greater than a semicircle is less than a right angle ; and the angle in a segment less than a semicircle is greater than a right angle.
Page 23 - Any two sides of a triangle are together greater than the third side.
Page 40 - EQUAL triangles upon the same base, and upon the same side of it, are between the same parallels.
Page 103 - If from any point without a circle two straight lines be drawn, one of which cuts the circle, and the other touches it; the rectangle contained by the whole line which cuts the circle, and the part of it without the circle, shall be equal to the square on the line which touches it.
Page 50 - PROP. I. THEOR. If there oe two straight lines, one of which is divided into any number of parts; the rectangle contained by the two straight lines, is equal to the rectangles contained by the undivided line, and the several parts of the divided line.
Page 28 - If two triangles have two angles of the one equal to two angles of the other, each to each, and also one side of the one equal to the corresponding side of the other, the triangles are congruent.