Euclid's Elements of Geometry: The First Six, the Eleventh and Twelfth Books |
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Page 5
... double to the fame thing , are equal to one another . 7. Things which are halves of the fame thing , are equal to one another . 8. Things which mutually agree with one another , are equal to one another s . 9. The whole is greater than ...
... double to the fame thing , are equal to one another . 7. Things which are halves of the fame thing , are equal to one another . 8. Things which mutually agree with one another , are equal to one another s . 9. The whole is greater than ...
Page 45
... double to the triangle ABC ; for the diameter A C [ by prop . 34. ] cuts it into halves : wherefore the parallelogram A B C D will be double to the triangle E B C. B C If therefore a parallelogram and a triangle have the fame bafe , and ...
... double to the triangle ABC ; for the diameter A C [ by prop . 34. ] cuts it into halves : wherefore the parallelogram A B C D will be double to the triangle E B C. B C If therefore a parallelogram and a triangle have the fame bafe , and ...
Page 46
... double to the triangle A E C. But [ by prop . 41. ] the parallelogram FECG is double to the triangle A EC ; for it has the fame bafe , and is between the fame parallels : Therefore [ by ax . 6. ] the parallelogram FE C G is double to ...
... double to the triangle A E C. But [ by prop . 41. ] the parallelogram FECG is double to the triangle A EC ; for it has the fame bafe , and is between the fame parallels : Therefore [ by ax . 6. ] the parallelogram FE C G is double to ...
Page 51
... double to the triangle FBC , fince they have the fame base FB , and are between the fame parallels FB , GC . But the doubles of equal things are themselves equal : therefore the parallelogram B L is equal to the fquare GB . After the ...
... double to the triangle FBC , fince they have the fame base FB , and are between the fame parallels FB , GC . But the doubles of equal things are themselves equal : therefore the parallelogram B L is equal to the fquare GB . After the ...
Page 82
... 1. ] the rectangle AG is equal to the rectangle GE , add CF , which is common , to both ; then the whole AF is equal to the whole CE : therefore the } F the rectangles AF , CE are double B to 82 Book II . Euclid's Elements .
... 1. ] the rectangle AG is equal to the rectangle GE , add CF , which is common , to both ; then the whole AF is equal to the whole CE : therefore the } F the rectangles AF , CE are double B to 82 Book II . Euclid's Elements .
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...