Euclid's Elements of Geometry: The First Six, the Eleventh and Twelfth Books |
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Seite 4
That a rhomboides , whose opposite sides and angles are equal , but is neither equal - fided nor right - angled 9 . 34. All four - fided figures besides these may be called trapeziunis . 35. Parallels are right lines , which being in ...
That a rhomboides , whose opposite sides and angles are equal , but is neither equal - fided nor right - angled 9 . 34. All four - fided figures besides these may be called trapeziunis . 35. Parallels are right lines , which being in ...
Seite 9
... and one triangle equal to the other triangle ; and the remaining angles of tive one fall be equal to the remaining angles of the cth.r , each to each , which are opposite to the equal fices w , Let the two triangles be A BC , D E F ...
... and one triangle equal to the other triangle ; and the remaining angles of tive one fall be equal to the remaining angles of the cth.r , each to each , which are opposite to the equal fices w , Let the two triangles be A BC , D E F ...
Seite 10
cach to each , which are opposite to the equal fides ; that is , the angle ABC to the angle D e F , and the angle A CB to the angle DFE . For if the triangle A B C be applied to the triangle e DF , D and the point A be put upon the ...
cach to each , which are opposite to the equal fides ; that is , the angle ABC to the angle D e F , and the angle A CB to the angle DFE . For if the triangle A B C be applied to the triangle e DF , D and the point A be put upon the ...
Seite 11
shall be equal to the triangle CGB ; and the remaining angles shall be equal to the remaining angles , each to each , which are opposite to the equal lides : Therefore the angle FBC is equal to the angle GC B , and the angle Bcc to the ...
shall be equal to the triangle CGB ; and the remaining angles shall be equal to the remaining angles , each to each , which are opposite to the equal lides : Therefore the angle FBC is equal to the angle GC B , and the angle Bcc to the ...
Seite 12
If two angles of a triangle be equal to one another , then mall the sides opposite to the equal angles be equal to one another . Let the triangle A B C have the angle A B C equal to the angle ACB . I say , the side A C will be equal to ...
If two angles of a triangle be equal to one another , then mall the sides opposite to the equal angles be equal to one another . Let the triangle A B C have the angle A B C equal to the angle ACB . I say , the side A C will be equal to ...
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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...