Euclid's Elements of Geometry: The First Six, the Eleventh and Twelfth Books |
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Página 13
... the lines AD , DB , having the same ends A , B with the two first lines AC , CB ; so that c A be equal to D A , both having the same end A : and ce be equal to De , both having the same end B : for join the right line cö .
... the lines AD , DB , having the same ends A , B with the two first lines AC , CB ; so that c A be equal to D A , both having the same end A : and ce be equal to De , both having the same end B : for join the right line cö .
Página 31
put the right line B G equal to £ D , and join Gc . E B Then because нс the fide B G is equal to the side D E , and the fide b c to the side E F , viz . the two fides B G , Bc equal to the two sides DE , EF , each to each ; and the ...
put the right line B G equal to £ D , and join Gc . E B Then because нс the fide B G is equal to the side D E , and the fide b c to the side E F , viz . the two fides B G , Bc equal to the two sides DE , EF , each to each ; and the ...
Página 38
Two right lines , which join two equal and parallel right lines , towards the same parts , are also themselves equal and paralleli . Let the right lines A C , B D join towards the fame parts the equal and parallel right lines A B ...
Two right lines , which join two equal and parallel right lines , towards the same parts , are also themselves equal and paralleli . Let the right lines A C , B D join towards the fame parts the equal and parallel right lines A B ...
Página 39
Therefore two right lines which join two equal and parallel right lines , towards the same parts , are themselves both equal and parallel . Which was to be demonstrated . ! If two right lines do not the same way join the equal parallel ...
Therefore two right lines which join two equal and parallel right lines , towards the same parts , are themselves both equal and parallel . Which was to be demonstrated . ! If two right lines do not the same way join the equal parallel ...
Página 42
For join BE , CH . Then because BC is equal to FG , А E and F G equal to EH ; thereH fore will bc be equal to E H. They are parallel too , and BE , CH joins them . But right lines which join equal and parallel right lines towards : the ...
For join BE , CH . Then because BC is equal to FG , А E and F G equal to EH ; thereH fore will bc be equal to E H. They are parallel too , and BE , CH joins them . But right lines which join equal and parallel right lines towards : the ...
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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...