Euclid's Elements of Geometry: The First Six, the Eleventh and Twelfth Books |
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Seite x
Prop . vii . at page 64. the Scholium at page 97. the Scholium at page 100. Prop : viü . at page 204 . Prop . ix . at page 205. the Scholium at page 106 . and the proposition . Prop . ix . at page 158. Prop . X. at page 160.
Prop . vii . at page 64. the Scholium at page 97. the Scholium at page 100. Prop : viü . at page 204 . Prop . ix . at page 205. the Scholium at page 106 . and the proposition . Prop . ix . at page 158. Prop . X. at page 160.
Seite 6
... were less than both the angles A E F , CFE on the left ; and since two different right lines cannot be drawn from the same point out of a given right line parallel to that given right line ; and since it is demonftrated at prop .
... were less than both the angles A E F , CFE on the left ; and since two different right lines cannot be drawn from the same point out of a given right line parallel to that given right line ; and since it is demonftrated at prop .
Seite 7
PROP . II . PROBL . To put a right line at a given point equal to a given right line . Let the given point be A , and the given right line be BC ; it is required to put a right line at the point a equal to the given right line Bc . Draw ...
PROP . II . PROBL . To put a right line at a given point equal to a given right line . Let the given point be A , and the given right line be BC ; it is required to put a right line at the point a equal to the given right line Bc . Draw ...
Seite 8
PROP . III . PROBL . Two unequal right lines being given , to take a right line from the greater equal to the lesser . ' . Let the two unequal right lines given be a B and c , whereof let A B be the greater ; it is required to take a ...
PROP . III . PROBL . Two unequal right lines being given , to take a right line from the greater equal to the lesser . ' . Let the two unequal right lines given be a B and c , whereof let A B be the greater ; it is required to take a ...
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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...