Euclid's Elements of Geometry: The First Six, the Eleventh and Twelfth Books |
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Seite 9
If two triangles have two sides of the ore equal to two sides of the other , each to each ; and bite one angle of the ... and the remaining angles of tive one fall be equal to the remaining angles of the cth.r , each to each , which are ...
If two triangles have two sides of the ore equal to two sides of the other , each to each ; and bite one angle of the ... and the remaining angles of tive one fall be equal to the remaining angles of the cth.r , each to each , which are ...
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 ... remaining angles will agree with the remaining angles , and therefore shall be equal to them , viz . the angle A BC ...
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 ... remaining angles will agree with the remaining angles , and therefore shall be equal to them , viz . the angle A BC ...
Seite 11
continue the equal fides A B , AC directly forwards to D and E : I say , the angle ABC is equal to the angle ACB ... shall be equal to the triangle CGB ; and the remaining angles shall be equal to the remaining angles , each to each ...
continue the equal fides A B , AC directly forwards to D and E : I say , the angle ABC is equal to the angle ACB ... shall be equal to the triangle CGB ; and the remaining angles shall be equal to the remaining angles , each to each ...
Seite 12
will be equal to the remaining angle a CB ; and they are at the base of the triangle A B C. But also it has been ... Therefore the angles at the base of iosceles triangles are equal to one another , and the equal right lines being ...
will be equal to the remaining angle a CB ; and they are at the base of the triangle A B C. But also it has been ... Therefore the angles at the base of iosceles triangles are equal to one another , and the equal right lines being ...
Seite 16
These therefore being taken away from the former , and there will remain [ by axiom 3. ] the angles e A F , E D F equal . Which was to be demonstrated . PROP . IX . PROBL . To biseEt or cut a given right - lined angle into two equal ...
These therefore being taken away from the former , and there will remain [ by axiom 3. ] the angles e A F , E D F equal . Which was to be demonstrated . PROP . IX . PROBL . To biseEt or cut a given right - lined angle into two equal ...
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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...