Euclid's Elements of Geometry: The First Six, the Eleventh and Twelfth Books |
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Seite 18
But when a right line standing upon a right line makes the adjacent angles equal to one anA D С E B В other , each of these equal angles is a right angle [ by def . 10. ] . Therefore each of the angles DCF , Fce is a right angle .
But when a right line standing upon a right line makes the adjacent angles equal to one anA D С E B В other , each of these equal angles is a right angle [ by def . 10. ] . Therefore each of the angles DCF , Fce is a right angle .
Seite 19
If a right line standing upon a right line makes angles , these angles hall either be two right angles , or ( botb together ] equal to two right angles d . For let any right line A B , standing upon the right line DC , make the angles ...
If a right line standing upon a right line makes angles , these angles hall either be two right angles , or ( botb together ] equal to two right angles d . For let any right line A B , standing upon the right line DC , make the angles ...
Seite 20
If therefore a right line standing upon a right line makes angles , these angles shall either be two right angles , or [ both together ] equal to two right angles . Which was to be demonstrated . . This proposition seems to defend upon ...
If therefore a right line standing upon a right line makes angles , these angles shall either be two right angles , or [ both together ] equal to two right angles . Which was to be demonstrated . . This proposition seems to defend upon ...
Seite 21
For because the right line A E stands upon the right line C D , D making the angles C E A , A E D. E Therefore the angles CEA , AED are [ by prop . 13. ] equal B to two right angles . Again , because the right line de stands upon the ...
For because the right line A E stands upon the right line C D , D making the angles C E A , A E D. E Therefore the angles CEA , AED are [ by prop . 13. ] equal B to two right angles . Again , because the right line de stands upon the ...
Seite 42
is equal to the parallelogram D BC F , for they stand both upon the fame base e c , and are between the same pa 8 C rallels BC , EF . But the triangle given triangle . 42 Euclid's Elements . Book I.
is equal to the parallelogram D BC F , for they stand both upon the fame base e c , and are between the same pa 8 C rallels BC , EF . But the triangle given triangle . 42 Euclid's Elements . Book I.
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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 cylinder definition demonſtrated deſcribed diameter difference divided double draw drawn equal equal angles equiangular equimultiples Euclid exceeds fall fame fides figure firſt folid fore 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 247 - 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 30 - 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 248 - 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 18 - 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 32 - 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 56 - 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 391 - 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 110 - If any two points be taken in the circumference of a circle, the straight line which joins them shall fall within the circle.
Seite 130 - When you have proved that the three angles of every triangle are equal to two right angles...
Seite 183 - 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...