Euclid's Elements of Geometry: The First Six, the Eleventh and Twelfth Books |
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Seite 8
Therefore because the point E is the centre of the circle CGH , the right line b c will be equal to the right line BG B [ by def . 15. ] . Again , because the point D is the centre of the circle ' GʻL K ; therefore D. L is equal to D G ...
Therefore because the point E is the centre of the circle CGH , the right line b c will be equal to the right line BG B [ by def . 15. ] . Again , because the point D is the centre of the circle ' GʻL K ; therefore D. L is equal to D G ...
Seite 10
For if the triangle A B C be applied to the triangle e DF , D and the point A be put upon the point D , 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 ...
For if the triangle A B C be applied to the triangle e DF , D and the point A be put upon the point D , 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 ...
Seite 12
3 * Scarborough fays , the latter part of this proposition seems not to be Euclid's , but put in by somebody elle ; because , says he , it is certain , that Euclid never laid down an elementary proposition useless in any part thereof ...
3 * Scarborough fays , the latter part of this proposition seems not to be Euclid's , but put in by somebody elle ; because , says he , it is certain , that Euclid never laid down an elementary proposition useless in any part thereof ...
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 , BC equal to two 1 right lines AC , CB , each to each ; and the angle DBC is equal to the angle ACB ...
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 , BC equal to two 1 right lines AC , CB , each to each ; and the angle DBC is equal to the angle ACB ...
Seite 15
Because in the triangle A e D , the two fides A E , DB are put equal ( for now the right line A E is the same with A B , which by the fuppofi- A D tion is equal to the right line de ) the angles A and D upon the base AD , will be [ by 5 ...
Because in the triangle A e D , the two fides A E , DB are put equal ( for now the right line A E is the same with A B , which by the fuppofi- A D tion is equal to the right line de ) the angles A and D upon the base AD , will be [ by 5 ...
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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...