Euclid's Elements of Geometry: The First Six, the Eleventh and Twelfth Books |
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Página xi
-Now that part of the Fifth Definition of the Fifth Book ( see the Definition itself in its Place ) which says , “ If the Multiple of the First Magni* cude be equal to the Multiple of the Second , che Multiple of the Third will be equal ...
-Now that part of the Fifth Definition of the Fifth Book ( see the Definition itself in its Place ) which says , “ If the Multiple of the First Magni* cude be equal to the Multiple of the Second , che Multiple of the Third will be equal ...
Página xii
Multiple of the Fourth , " Cannot exist when the Magnitudes are incommenfurable ; because when the First and Second , and the Third and Fourthi Terms of Two equal Ratios , or Four Proportionals are incommensurable , no Number of Times ...
Multiple of the Fourth , " Cannot exist when the Magnitudes are incommenfurable ; because when the First and Second , and the Third and Fourthi Terms of Two equal Ratios , or Four Proportionals are incommensurable , no Number of Times ...
Página xiii
... whether the Magnitudes be commensurable or incommensurable , by a clear Definition of Proportionality very , different from the Fifth of the Fifth Book , and by help of a few of the Propositions of the First and Third Books .
... whether the Magnitudes be commensurable or incommensurable , by a clear Definition of Proportionality very , different from the Fifth of the Fifth Book , and by help of a few of the Propositions of the First and Third Books .
Página 3
Do not thole describe a superficies best , who say it is what is generated by the motion of a line , not moving end ways , or in the direction of itself ? e This , as well as the third definition , of the ...
Do not thole describe a superficies best , who say it is what is generated by the motion of a line , not moving end ways , or in the direction of itself ? e This , as well as the third definition , of the ...
Página 6
... certainly and most evidently , when two such angles are less than two right angles , the right lines which are crossed by the third right line ( with which they make these angles ) will not be parallel , and so muft neceffarily meet ...
... certainly and most evidently , when two such angles are less than two right angles , the right lines which are crossed by the third right line ( with which they make these angles ) will not be parallel , and so muft neceffarily meet ...
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Euclid's Elements of Geometry: The First Six, the Eleventh and Twelfth Books Euclid,David Gregory Sin vista previa disponible - 2016 |
Términos y frases comunes
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
Pasajes populares
Página 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.
Página 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...
Página 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.
Página 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.
Página 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.
Página 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.
Página 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...
Página 108 - If any two points be taken in the circumference of a circle, the straight line which joins them shall fall within the circle.
Página 128 - When you have proved that the three angles of every triangle are equal to two right angles...
Página 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...