Euclid's Elements of Geometry: The First Six, the Eleventh and Twelfth Books |
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Page 276
If a parallelogram be taken away from a parallelogram similar to the whole , alike
fituate , and both having one common angle : I say they will also both have the
same common diameter . For from the parallelogram Abcd let the parallelogram
A ...
If a parallelogram be taken away from a parallelogram similar to the whole , alike
fituate , and both having one common angle : I say they will also both have the
same common diameter . For from the parallelogram Abcd let the parallelogram
A ...
Page 277
Therefore the parallelograms ABCD , KG have not both the fame common
diameter . Wherefore the parallelograms A BCD , A EFG have both the same
common diameter . If therefore a parallelogram be taken away from a par .
allelogram ...
Therefore the parallelograms ABCD , KG have not both the fame common
diameter . Wherefore the parallelograms A BCD , A EFG have both the same
common diameter . If therefore a parallelogram be taken away from a par .
allelogram ...
Page 300
Let the right line A c be the common base of the segments A B C , A FC of a circle
, and let the right line ECD cutting the circle , make the angle ACD equal to the
angle ABC in the segment ABC , or the angle ACE equal to the angle Arc in the ...
Let the right line A c be the common base of the segments A B C , A FC of a circle
, and let the right line ECD cutting the circle , make the angle ACD equal to the
angle ABC in the segment ABC , or the angle ACE equal to the angle Arc in the ...
Page 330
Hi For let the plane de pass thro ' the right line A B , and let the right line ce be the
common fection of the plane DE and the given plane : Take any point F in c E ,
and from the same draw Fg in the plane G A H De at right angles to CE .
Hi For let the plane de pass thro ' the right line A B , and let the right line ce be the
common fection of the plane DE and the given plane : Take any point F in c E ,
and from the same draw Fg in the plane G A H De at right angles to CE .
Page 457
33. where he first uses the word Side of a parallelepipedon , he calls the side of
the parallelogram , which is the base of that solid , the side of the
parallelepipedon . As this is somewhat contrary to common conception , I think it
might not be ...
33. where he first uses the word Side of a parallelepipedon , he calls the side of
the parallelogram , which is the base of that solid , the side of the
parallelepipedon . As this is somewhat contrary to common conception , I think it
might not be ...
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Common terms and phrases
A B C ABCD added alſo altitude baſe becauſe centre circle circumference common cone 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
Popular passages
Page 247 - 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.
Page 30 - 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...
Page 248 - 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.
Page 18 - 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.
Page 32 - 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.
Page 56 - 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.
Page 391 - 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...
Page 110 - If any two points be taken in the circumference of a circle, the straight line which joins them shall fall within the circle.
Page 130 - When you have proved that the three angles of every triangle are equal to two right angles...
Page 183 - 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...
Bibliographic information
| Title | Euclid's Elements of Geometry: The First Six, the Eleventh and Twelfth Books |
| Authors | Euclid, Edmund Stone |
| Translated by | Edmund Stone |
| Edition | 2 |
| Publisher | J. Rivington, 1765 |
| Original from | the University of Michigan |
| Digitized | 23 Jun 2007 |
| Length | 464 pages |
| Export Citation | BiBTeX EndNote RefMan |