Euclid's Elements of Geometry: The First Six, the Eleventh and Twelfth Books |
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Page 14
... same ends with the first right lines . Which was to be demonstrated . Although this 7th propofition may be thought to be of no great importance in itfelf , yet its ufe in demonftrating the 8th propofition makes it both valuable and ...
... same ends with the first right lines . Which was to be demonstrated . Although this 7th propofition may be thought to be of no great importance in itfelf , yet its ufe in demonftrating the 8th propofition makes it both valuable and ...
Page 33
... same manner we de- monftrate , that these lines will not meet towards a c : but right lines , which being either way produced , and do not meet , are [ by def . 35. ] parallel to one another . Therefore A B is parallel to CD , Wherefore ...
... same manner we de- monftrate , that these lines will not meet towards a c : but right lines , which being either way produced , and do not meet , are [ by def . 35. ] parallel to one another . Therefore A B is parallel to CD , Wherefore ...
Page 41
... same base , and between the fame parallels , are the one equal to the other . Which was to be demonstrated . PROP . XXXVI . THEOR . Parallelograms conftituted upon equal bases , and be- tween the fame parallels , are equal the one to ...
... same base , and between the fame parallels , are the one equal to the other . Which was to be demonstrated . PROP . XXXVI . THEOR . Parallelograms conftituted upon equal bases , and be- tween the fame parallels , are equal the one to ...
Page 44
... same parallels . For draw A D : I fay , this is parallel to B C. A E D For if not , through the point A [ by prop . 31. ] draw the right line A E parallel to the right line B C , and draw E C. Then [ by prop . 37. ] the triangle ABC is ...
... same parallels . For draw A D : I fay , this is parallel to B C. A E D For if not , through the point A [ by prop . 31. ] draw the right line A E parallel to the right line B C , and draw E C. Then [ by prop . 37. ] the triangle ABC is ...
Page 51
... same reason AB and Aн make but one right line . And becaufe the angle DBC [ by ax . 10. ] is equal to the angle F B A , for they are both right angles . Add the angle ABC , which is common ; then will the whole angle DBA be equal to the ...
... same reason AB and Aн make but one right line . And becaufe the angle DBC [ by ax . 10. ] is equal to the angle F B A , for they are both right angles . Add the angle ABC , which is common ; then will the whole angle DBA be equal to the ...
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...