Euclid's Elements of Geometry: The First Six, the Eleventh and Twelfth Books |
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Page 316
If two right lines mutually cut each other , they are both in the same plane ; also
every triangle lies in one planek . For let two right lines A B , CD cut one another
in the point E : I say the right lines AB , CD are both in the fame plane , also every
...
If two right lines mutually cut each other , they are both in the same plane ; also
every triangle lies in one planek . For let two right lines A B , CD cut one another
in the point E : I say the right lines AB , CD are both in the fame plane , also every
...
Page 322
ED will be perpendicular to the plane drawn thro ' BD , DA ; and will be at right
angles to all right lines which touch it , and are in that same plane . But dc is in
the plane drawn thro ' BA , AD , because AB , BD [ by 2. 11. ) are in the plane
drawn ...
ED will be perpendicular to the plane drawn thro ' BD , DA ; and will be at right
angles to all right lines which touch it , and are in that same plane . But dc is in
the plane drawn thro ' BA , AD , because AB , BD [ by 2. 11. ) are in the plane
drawn ...
Page 324
... Twelfth Books Euclid, Edmund Stone. If therefore ad be also perpendicular to
the given plane ; what was required will then be done : But if H it be not , [ by II . 1.
) draw de in the given plane from the point d'y perpendicular to Bc ; and ( by 12 .
... Twelfth Books Euclid, Edmund Stone. If therefore ad be also perpendicular to
the given plane ; what was required will then be done : But if H it be not , [ by II . 1.
) draw de in the given plane from the point d'y perpendicular to Bc ; and ( by 12 .
Page 325
A plane being given , and a point given in it ; to ere & t a right line from that point
at right ' angles to tbat planem . Let A be the given point in a given plane : It is
required to erect a right line from that point ac right anglés to that plane .
Conceive ...
A plane being given , and a point given in it ; to ere & t a right line from that point
at right ' angles to tbat planem . Let A be the given point in a given plane : It is
required to erect a right line from that point ac right anglés to that plane .
Conceive ...
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 .
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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 |