Euclid's Elements of Geometry: The First Six, the Eleventh and Twelfth Books |
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Seite 4
... drawn from that point to ( or rather towards ) that given right line , is parallel to it . But Euclid's definition of parallels is in general the best ; though in fome particular instances , these others are not without their use .
... drawn from that point to ( or rather towards ) that given right line , is parallel to it . But Euclid's definition of parallels is in general the best ; though in fome particular instances , these others are not without their use .
Seite 6
... who have demonstrated it , have been only triling ; and instead of making it more evident , have more obscured it . ---- Since two right lines A B , CD in the same plane , must necessarily meet or ' A be parallel ; and if they meet ...
... who have demonstrated it , have been only triling ; and instead of making it more evident , have more obscured it . ---- Since two right lines A B , CD in the same plane , must necessarily meet or ' A be parallel ; and if they meet ...
Seite 32
For if it be not parallel , the lines A B , DC produced will meet either towards B D Or A C ; let them be produced towards A E B B D , and meet in the point G. Now the angle AEF being the external angle of the triangle c F EGF ...
For if it be not parallel , the lines A B , DC produced will meet either towards B D Or A C ; let them be produced towards A E B B D , and meet in the point G. Now the angle AEF being the external angle of the triangle c F EGF ...
Seite 33
parallel to one another . Therefore A R is parallel to CD , Wherefore if a right line falling upon two right lines makes the alternate angles equal to one another , these two right lines shall be parallel . Which was to be demonstrated ...
parallel to one another . Therefore A R is parallel to CD , Wherefore if a right line falling upon two right lines makes the alternate angles equal to one another , these two right lines shall be parallel . Which was to be demonstrated ...
Seite 34
If a right line falls upon two parallel right lines , it makes the alternate angles equal to one another ; the outward angle equal to the inward and opposite angle on the same side ; and the inward angles on the same fide together equal ...
If a right line falls upon two parallel right lines , it makes the alternate angles equal to one another ; the outward angle equal to the inward and opposite angle on the same side ; and the inward angles on the same fide together equal ...
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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...