Euclid's Elements of Geometry: The First Six, the Eleventh and Twelfth Books |
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Seite 39
The opposite sides and angles of any parallelogram or figure bounded by parallel lines , are equal to one another , and a diameter bisects it " . Let there be a parallelogram ACDB , and its diameter BC : I say , the opposite sides and ...
The opposite sides and angles of any parallelogram or figure bounded by parallel lines , are equal to one another , and a diameter bisects it " . Let there be a parallelogram ACDB , and its diameter BC : I say , the opposite sides and ...
Seite 40
It has been also demonstrated , that the angle B A c is equal to the anzie BDS . Therefore the opposite fides and angles of any parallelogram ( or four - fided figure bounded by parallel lines ) are equal .
It has been also demonstrated , that the angle B A c is equal to the anzie BDS . Therefore the opposite fides and angles of any parallelogram ( or four - fided figure bounded by parallel lines ) are equal .
Seite 41
Parallelograms constituted upon the same base , and between the same parallels , are the one equal to the other . ... and between the fame parallels AF , BC : I say , the parallelogram A B C D is equal to the parallelogram E BCF .
Parallelograms constituted upon the same base , and between the same parallels , are the one equal to the other . ... and between the fame parallels AF , BC : I say , the parallelogram A B C D is equal to the parallelogram E BCF .
Seite 42
rallels A H , BG : I say , the parallelograms A B C D , EF G H are equal to one another . For join BE , CH . ... Therefore EB , ch are both equal and parallel ; and so E B C H is a parallelogram , which [ by prop . 35. ] ...
rallels A H , BG : I say , the parallelograms A B C D , EF G H are equal to one another . For join BE , CH . ... Therefore EB , ch are both equal and parallel ; and so E B C H is a parallelogram , which [ by prop . 35. ] ...
Seite 43
angle A B C is the one half of the parallelogram e BCA ; since the diameter AB cuts into halves , and the triangle DBC the one half of the parallelogram DBCF ; because [ by prop . 34. ] the diameter Dc cuts it into halves .
angle A B C is the one half of the parallelogram e BCA ; since the diameter AB cuts into halves , and the triangle DBC the one half of the parallelogram DBCF ; because [ by prop . 34. ] the diameter Dc cuts it into halves .
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Euclid's Elements of Geometry: The First Six, the Eleventh and Twelfth Books Euclid,David Gregory Keine Leseprobe verfügbar - 2016 |
Häufige Begriffe und Wortgruppen
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
Beliebte Passagen
Seite 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.
Seite 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...
Seite 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.
Seite 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.
Seite 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.
Seite 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.
Seite 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...
Seite 108 - If any two points be taken in the circumference of a circle, the straight line which joins them shall fall within the circle.
Seite 128 - When you have proved that the three angles of every triangle are equal to two right angles...
Seite 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...