Euclid's Elements of Geometry: The First Six, the Eleventh and Twelfth Books |
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Page 6
... right lines A B , CD in the fame plane , muft neceffarily meet or be parallel ; and if they meet , it B muft either be to the right or left of the right line E F falling upon D them , what man of common fenfe would fay they would meet ...
... right lines A B , CD in the fame plane , muft neceffarily meet or be parallel ; and if they meet , it B muft either be to the right or left of the right line E F falling upon D them , what man of common fenfe would fay they would meet ...
Page 7
... right line . ETA B be a given finite right line : it is required to conftitute an equilateral triangle upon the right line C From the centre A , with the distance A B , let the circle BCD be described [ by poftul . 3. ] and again from ...
... right line . ETA B be a given finite right line : it is required to conftitute an equilateral triangle upon the right line C From the centre A , with the distance A B , let the circle BCD be described [ by poftul . 3. ] and again from ...
Page 9
The First Six, the Eleventh and Twelfth Books Euclid. of the right lines A E and c is equal to the right line AD ; wherefore the right line A E is alio equal to the right line c . Therefore two unequal right lines , A B and C , being ...
The First Six, the Eleventh and Twelfth Books Euclid. of the right lines A E and c is equal to the right line AD ; wherefore the right line A E is alio equal to the right line c . Therefore two unequal right lines , A B and C , being ...
Page 10
... right line A B upon the right line D E , then fhall the point в agree with the point E ; because A B is equal to DE : But fince F the right line A B agrees with D E , the right line A c fhall also agree with DF , because the angle BAC ...
... right line A B upon the right line D E , then fhall the point в agree with the point E ; because A B is equal to DE : But fince F the right line A B agrees with D E , the right line A c fhall also agree with DF , because the angle BAC ...
Page 11
... right line BD , let there be taken any point as F ; and from the greater line A E , let be taken A G equal to AF the lefs [ by prop . 3. ] and draw the right lines FC , G B. D B E Therefore becaufe A F is equal to AG , and the right line ...
... right line BD , let there be taken any point as F ; and from the greater line A E , let be taken A G equal to AF the lefs [ by prop . 3. ] and draw the right lines FC , G B. D B E Therefore becaufe A F is equal to AG , and the right line ...
Other editions - View all
Euclid's Elements of Geometry: The First Six, the Eleventh and Twelfth Books Euclid,David Gregory No preview available - 2023 |
Euclid's Elements of Geometry: The First Six, the Eleventh and Twelfth Books Euclid,David Gregory No preview available - 2023 |
Euclid's Elements of Geometry: The First Six, the Eleventh and Twelfth Books Euclid,David Gregory No preview available - 2016 |
Common terms and phrases
A B C D alfo alſo angle ABC becauſe the angle bifected centre circle A B C circumference cone confequent cylinder defcribed demonftrated diameter equal angles equiangular equimultiples Euclid EUCLID's ELEMENTS fame altitude fame multiple fame ratio fame reafon fecond fegment femidiameter fhall fides A B fimilar fince firft firſt fixth folid angle folid parallelepipedon fome fphere ftand given circle given right line given triangle greater infcribed interfect join leffer lefs leſs parallel parallelogram perpendicular polygon prifm PROP propofition proportional pyramid rectangle contained regular polygon remaining angle right angles right line A B right lined figure right-lined SCHOLIUM ſquare thefe THEOR theſe thofe thoſe trapezium triangle ABC twice the fquare vertex the point Wherefore whofe bafe 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...