The Elements of Euclid: Viz, the First Six Books, Together with the Eleventh and Twelfth ; the Errors, by which Theon, Or Others, Have Long Ago Vitiated These Books, are Corrected, and Some of Euclid's Demonstrations are Restored ; Also the Book of Euclid's Data, in Like Manner CorrectedDesilver, 1829 - 516 sider |
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Side 122
... magnitudes be of all the other : For the same demonstration ' holds in any number of magnitudes , which was here applied to ' two . ' Q. E. D. PROP . II . THEOR . If the first magnitude be the same multiple of the se- cond that the ...
... magnitudes be of all the other : For the same demonstration ' holds in any number of magnitudes , which was here applied to ' two . ' Q. E. D. PROP . II . THEOR . If the first magnitude be the same multiple of the se- cond that the ...
Side 123
... magnitudes in EF equal to A ; as are in GH equal to C : let EF be di- vided into the magnitudes EK , KF , each equal to A , and GH into GL , LH , each equal to C : the number therefore of the magnitudes EK , KF , shall be equal to ' the ...
... magnitudes in EF equal to A ; as are in GH equal to C : let EF be di- vided into the magnitudes EK , KF , each equal to A , and GH into GL , LH , each equal to C : the number therefore of the magnitudes EK , KF , shall be equal to ' the ...
Side 125
... magnitude taken from the first is of a magnitude taken from the other ; the remainder shall be the same multiple of the remainder , that the whole is of the whole . Let the magnitude AB be the same multi- ple of CD , that AE taken from ...
... magnitude taken from the first is of a magnitude taken from the other ; the remainder shall be the same multiple of the remainder , that the whole is of the whole . Let the magnitude AB be the same multi- ple of CD , that AE taken from ...
Side 126
... magnitude , & c . Q. E. D. PROP . VI . THEOR . Ir two magnitudes be equimultiples of two others , and if equimultiples of these be taken from the first two , the remainders are either equal to these others , or equimulti- ples of them ...
... magnitude , & c . Q. E. D. PROP . VI . THEOR . Ir two magnitudes be equimultiples of two others , and if equimultiples of these be taken from the first two , the remainders are either equal to these others , or equimulti- ples of them ...
Side 127
... magnitudes be proportionals , they are propor- tionals also when taken inversely . * If the magnitude A be to B , as C is to D , then also inversely B is to A , as D to C. Take of B and D any equimultiples whatever E and F ; and of A ...
... magnitudes be proportionals , they are propor- tionals also when taken inversely . * If the magnitude A be to B , as C is to D , then also inversely B is to A , as D to C. Take of B and D any equimultiples whatever E and F ; and of A ...
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The Elements of Euclid: Viz, the First Six Books, Together with the Eleventh ... Robert Simson,Euclid Euclid Ingen forhåndsvisning tilgjengelig - 2018 |
Vanlige uttrykk og setninger
altitude angle ABC angle BAC base BC BC is equal BC is given bisected centre circle ABCD circumference co-sine cone cylinder demonstrated described diameter draw drawn equal angles equiangular equimultiples Euclid ex æquali 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 multiple parallel parallelogram parallelogram AC perpendicular point F polygon prism proportionals proposition Q. E. D. PROP radius ratio of AE rectangle CB rectangle contained rectilineal figure remaining angle right angles segment sides BA similar sine solid angle solid parallelopipeds square of AC straight line AB straight line BC tangent THEOR third triangle ABC triplicate ratio vertex wherefore
Populære avsnitt
Side 9 - Let it be granted that a straight line may be drawn from any one point to any other point.
Side 81 - The angles in the same segment of a circle are equal to one another.
Side 315 - Equiangular parallelograms have to one another the ratio which is compounded of the ratios of their sides.
Side 33 - All the interior angles of any rectilineal figure, together with four right angles, are equal to twice as many right angles as the figure has sides.
Side 49 - If a straight line be divided into any two parts, the rectangle contained by the whole and one of the parts, is equal to the rectangle contained by the two parts, together with the square of the aforesaid part.
Side 96 - 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 of the line which touches it.
Side 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.
Side 22 - ANY two angles of a triangle are together less than two right angles.
Side 25 - Let A, B, C be the three given straight lines, of which any two whatever are greater than the third, viz.
Side 24 - Any two sides of a triangle are together greater than the third side.