Euclid's Elements of Geometry: The First Six, the Eleventh and Twelfth Books |
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Página 6
If both the angles E , F on the right were less than both the angles A E F , CFE on the left ; and since two different right lines cannot be drawn from the same point out of a given right line parallel to that given right line ...
If both the angles E , F on the right were less than both the angles A E F , CFE on the left ; and since two different right lines cannot be drawn from the same point out of a given right line parallel to that given right line ...
Página 13
Two right lines cannot be corostituted on the same right line equal to two other right lines , esch to ecch , ct different points on the same side , and having the Jamne ends with the first right lines ' .
Two right lines cannot be corostituted on the same right line equal to two other right lines , esch to ecch , ct different points on the same side , and having the Jamne ends with the first right lines ' .
Página 14
at different points on the same side , and having the same ends with the first right lines . Which was to be demonstrated . y Although this 7th proposition may be thought to be of no great importance in itself , yet its ule in ...
at different points on the same side , and having the same ends with the first right lines . Which was to be demonstrated . y Although this 7th proposition may be thought to be of no great importance in itself , yet its ule in ...
Página 20
... that so much as the angle A B D exceeds the right angle E B D , by so much is the remaining angle A B C exceeded by the right angle E BC ; for as there the angle A B E is the excess , so is the same angle A B E here the deficiency .
... that so much as the angle A B D exceeds the right angle E B D , by so much is the remaining angle A B C exceeded by the right angle E BC ; for as there the angle A B E is the excess , so is the same angle A B E here the deficiency .
Página 33
After the same manner we demonstrate , that these lines will not meet towards a c : but right lines , which being either way produced , and do not meet , are [ by def . 35. ] parallel to one another . Therefore A R is parallel to CD ...
After the same manner we demonstrate , that these lines will not meet towards a c : but right lines , which being either way produced , and do not meet , are [ by def . 35. ] parallel to one another . Therefore A R is parallel to CD ...
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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...