Euclid's Elements of Geometry: The First Six, the Eleventh and Twelfth Books |
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Página 9
If two triangles have two sides of the ore equal to two sides of the other , each to each ; and bite one angle of the one equal to one riigle of the ether , viz . that which is contained 1.7.der the equal lir's ; then spall the base of ...
If two triangles have two sides of the ore equal to two sides of the other , each to each ; and bite one angle of the one equal to one riigle of the ether , viz . that which is contained 1.7.der the equal lir's ; then spall the base of ...
Página 10
Therefore the base ec agrees with the base e F , and accordingly is equal to it . Therefore the whole triangle ABC agrees with the whole triangle D E F , and will be equal to the same ; and the remaining angles will agree with the ...
Therefore the base ec agrees with the base e F , and accordingly is equal to it . Therefore the whole triangle ABC agrees with the whole triangle D E F , and will be equal to the same ; and the remaining angles will agree with the ...
Página 11
The angles at the base of isosceles triangles are equal to one another ; and the equal right lines being produced , the angles under ibe baje sisall be equal to one another x Let Aec be an isosceles triangle , having the side A B equal ...
The angles at the base of isosceles triangles are equal to one another ; and the equal right lines being produced , the angles under ibe baje sisall be equal to one another x Let Aec be an isosceles triangle , having the side A B equal ...
Página 12
will be equal to the remaining angle a CB ; and they are at the base of the triangle A B C. But also it has been demonstrated , that the angle F B c is equal to the angle G CB , and they are under the base . Therefore the angles at the ...
will be equal to the remaining angle a CB ; and they are at the base of the triangle A B C. But also it has been demonstrated , that the angle F B c is equal to the angle G CB , and they are under the base . Therefore the angles at the ...
Página 14
If two triangles have two sides of the one equal to two sides of the other , each to each , and have also equal bases , then fall the angle contained by the equal sides of the ore triangle , be equal to the angle contained by the equal ...
If two triangles have two sides of the one equal to two sides of the other , each to each , and have also equal bases , then fall the angle contained by the equal sides of the ore triangle , be equal to the angle contained by the equal ...
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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...