Euclid's Elements of Geometry: The First Six, the Eleventh and Twelfth Books |
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Página 3
Some call a right line the shortest of all lines that have the fame extreme points or bounds ; others , that it is that line whose parts all tend the same way , or lie in the same direction , or of which no point in it is raised or ...
Some call a right line the shortest of all lines that have the fame extreme points or bounds ; others , that it is that line whose parts all tend the same way , or lie in the same direction , or of which no point in it is raised or ...
Página 6
If right lines which are parallel , that is , never meet , make the two inward angles on the fame side of a right line , falling upon them , both together equal to two right angles , certainly and most evidently , when two such angles ...
If right lines which are parallel , that is , never meet , make the two inward angles on the fame side of a right line , falling upon them , both together equal to two right angles , certainly and most evidently , when two such angles ...
Página 13
Therefore two right lines cannot be constituted upon the fame right line equal to two other right lines , each to each , D at See bommandines Bruchid . at different points on the same side , and having Book I. Euclid's Elements . 13.
Therefore two right lines cannot be constituted upon the fame right line equal to two other right lines , each to each , D at See bommandines Bruchid . at different points on the same side , and having Book I. Euclid's Elements . 13.
Página 17
Let there be a given right line a B , and let the given point in the fame be c ; it is required to draw a right line from the given point c at right angles to the right line A B. In the right line A B let there be taken any point D ...
Let there be a given right line a B , and let the given point in the fame be c ; it is required to draw a right line from the given point c at right angles to the right line A B. In the right line A B let there be taken any point D ...
Página 19
... A B C will be equal to the three angles D B E , EBA , A B C. But the angles CBE , EBD have been proved to be equal to the fame three angles ; and things which are equal to the fame thing , are equal to one another .
... A B C will be equal to the three angles D B E , EBA , A B C. But the angles CBE , EBD have been proved to be equal to the fame three angles ; and things which are equal to the fame thing , are equal to one another .
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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...