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 5
... magnitude , placed in the same order ; but neither is this universally true , except in the case in which the solid angles are contained by no more than three plane angles ; nor of this case is there any Demonstration in the Elements we ...
... magnitude , placed in the same order ; but neither is this universally true , except in the case in which the solid angles are contained by no more than three plane angles ; nor of this case is there any Demonstration in the Elements we ...
Side 117
... magnitude is said to be a part of a greater magnitude , when the less measures the greater , that is , " when the less is contained a certain number of times exactly in the greater . ' II . A greater magnitude is said to be a multiple ...
... magnitude is said to be a part of a greater magnitude , when the less measures the greater , that is , " when the less is contained a certain number of times exactly in the greater . ' II . A greater magnitude is said to be a multiple ...
Side 118
... magnitude has to the fourth ; and , on the contrary , the third is said to have to the fourth a less ratio than the ... magnitude . For example , if A , B , C , D be four magnitudes of the same kind , the first A is said to have to the ...
... magnitude has to the fourth ; and , on the contrary , the third is said to have to the fourth a less ratio than the ... magnitude . For example , if A , B , C , D be four magnitudes of the same kind , the first A is said to have to the ...
Side 120
... magnitudes are taken two and two . ' XIX . Ex æquali , from equality ; this term is used simply by itself , when the first magnitude is to the second of the first rank , as the first to the second of the other rank : and as the second ...
... magnitudes are taken two and two . ' XIX . Ex æquali , from equality ; this term is used simply by itself , when the first magnitude is to the second of the first rank , as the first to the second of the other rank : and as the second ...
Side 121
... magnitude is greater than the same mul- tiple of a less . IV . That magnitude of which a multiple is greater than the same multiple of another , is greater than that other magnitude . PROP . I. THEOR . IF any number of magnitudes be ...
... magnitude is greater than the same mul- tiple of a less . IV . That magnitude of which a multiple is greater than the same multiple of another , is greater than that other magnitude . PROP . I. THEOR . IF any number of magnitudes be ...
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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.