Euclid's Elements of Geometry: The First Six, the Eleventh and Twelfth Books |
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31. for Equimultiples , r . Multiples . P. 436. 1. 13. 25. 27 . for Equimultiples , r . Multiples . P. 444. for Addition , r . Additions . P. 447. the Letter E is wanted in the Fig . P. 448. I. 21. for Figures , r . Figure . P. 451. l .
31. for Equimultiples , r . Multiples . P. 436. 1. 13. 25. 27 . for Equimultiples , r . Multiples . P. 444. for Addition , r . Additions . P. 447. the Letter E is wanted in the Fig . P. 448. I. 21. for Figures , r . Figure . P. 451. l .
Seite 206
Four magnitudes are said to be in the fame ratio , the first to the second , and the third to the fourth : When the equimultiples of the first and third compared with the equiAs some take the numerical exponent or measure of a ratio to ...
Four magnitudes are said to be in the fame ratio , the first to the second , and the third to the fourth : When the equimultiples of the first and third compared with the equiAs some take the numerical exponent or measure of a ratio to ...
Seite 207
N. B. Instead of the word equimultiples it would be better to say equal multiples the meaning of this word being easier understood than of that word . 6. Magnitudes which are in , or have the same ratio , are called proportionals .
N. B. Instead of the word equimultiples it would be better to say equal multiples the meaning of this word being easier understood than of that word . 6. Magnitudes which are in , or have the same ratio , are called proportionals .
Seite 208
But when amongst the equimultiples ( of four magnitudes ) the multiple of the first ( magnitude ] shall exceed that of the second , but the multiple of the third shall not exceed that of the fourth ; then the first magnitude is said to ...
But when amongst the equimultiples ( of four magnitudes ) the multiple of the first ( magnitude ] shall exceed that of the second , but the multiple of the third shall not exceed that of the fourth ; then the first magnitude is said to ...
Seite 209
... what condition four magnitudes ought to have when the ratio of the first to the second is greater than that of the third to the fourth , saying that taking equimultiples of the first and third , and of the fecond and fourth .
... what condition four magnitudes ought to have when the ratio of the first to the second is greater than that of the third to the fourth , saying that taking equimultiples of the first and third , and of the fecond and fourth .
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Euclid's Elements of Geometry: The First Six, the Eleventh and Twelfth Books Euclid,David Gregory Keine Leseprobe verfügbar - 2016 |
Häufige Begriffe und Wortgruppen
A B C ABCD added alſo altitude baſe becauſe centre circle circumference common cone continue cylinder definition demonſtrated deſcribed diameter difference divided double draw drawn equal equal angles equiangular equimultiples Euclid exceeds fall fame fides figure firſt folid fore four fourth given right line greater half inſcribed join leſs magnitudes manner meet multiple oppoſite parallel parallelogram perpendicular plane polygon priſms PROP proportional propoſition proved pyramid ratio rectangle remaining angle right angles right line A B right lined figure ſame ſay ſecond ſegment ſhall ſides ſimilar ſince ſolid ſome ſphere ſquare ſtand ſum taken THEOR theſe third thoſe thro touch triangle triangle ABC twice vertex Wherefore whole whoſe baſe
Beliebte Passagen
Seite 245 - 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.
Seite 28 - 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...
Seite 246 - But it was proved that the angle AGB is equal to the angle at F ; therefore the angle at F is greater than a right angle : But by the hypothesis, it is less than a right angle ; which is absurd.
Seite 16 - When a straight line set up on a straight line makes the adjacent angles equal to one another, each of the equal angles is right, and the straight line standing on the other is called a perpendicular to that on which it stands.
Seite 30 - Let the straight line EF, which falls upon the two straight lines AB, CD, make the alternate angles AEF, EFD equal to one another; AB is parallel to CD.
Seite 54 - 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.
Seite 389 - KL: but the cylinder CM is equal to the cylinder EB, and the axis LN to the axis GH; therefore as the cylinder EB to...
Seite 108 - If any two points be taken in the circumference of a circle, the straight line which joins them shall fall within the circle.
Seite 128 - When you have proved that the three angles of every triangle are equal to two right angles...
Seite 181 - FK : in the same manner it may be demonstrated, that FL, FM, FG are each of them equal to FH, or FK : therefore the five straight lines FG, FH, FK, FL, FM are equal to one another : wherefore the circle described from the centre F, at the distance of...