Euclid's Elements of Geometry: The First Six, the Eleventh and Twelfth Books |
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Seite 6
gles , those right lines , being infinitely produced , do meet on that fide where the angles are less than two right angles " , 12 ... Since two right lines A B , CD in the same plane , must necessarily meet or be parallel ; and if they ...
gles , those right lines , being infinitely produced , do meet on that fide where the angles are less than two right angles " , 12 ... Since two right lines A B , CD in the same plane , must necessarily meet or be parallel ; and if they ...
Seite 7
ET A B be a given finite right line : it is required to constitute an equilateral triangle upon the right line A B. From the centre A , with the distance A B , let the circle BC D be described [ by poftul . 3. ) ...
ET A B be a given finite right line : it is required to constitute an equilateral triangle upon the right line A B. From the centre A , with the distance A B , let the circle BC D be described [ by poftul . 3. ) ...
Seite 9
of the right lines A E and c is equal to the right line AD ; wherefore ihe right line A E is alio equal to the righi line c . Therefore two unequal right lines , A B and c , being given , there is taken from the greater A B , a line ...
of the right lines A E and c is equal to the right line AD ; wherefore ihe right line A E is alio equal to the righi line c . Therefore two unequal right lines , A B and c , being given , there is taken from the greater A B , a line ...
Seite 10
... and the right line A B upon the right line DE , then shall the point B agree with the point E ; because A B is equal to de : But since B CE F the right line A B agrees with DE , the right line a c shall also agree with DF , because ...
... and the right line A B upon the right line DE , then shall the point B agree with the point E ; because A B is equal to de : But since B CE F the right line A B agrees with DE , the right line a c shall also agree with DF , because ...
Seite 13
Then , because D B is equal to the right line A c , and the right line Bc is a common side , there will be two right lines D B ... Therefore the right line A B is not unequal to the right line A C ; they are consequently equal .
Then , because D B is equal to the right line A c , and the right line Bc is a common side , there will be two right lines D B ... Therefore the right line A B is not unequal to the right line A C ; they are consequently 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 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...