Euclid's Elements of Geometry: The First Six, the Eleventh and Twelfth Books |
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Page 83
... double to the rectangle AF . But twice the rectangle under AB , BC is double to AF : for [ by cor . 4. 2. ] B F is equal to B C. Therefore the gno- A H G K M N D mon KLM , and the fquare CF , are equal to twice the rectangle under the ...
... double to the rectangle AF . But twice the rectangle under AB , BC is double to AF : for [ by cor . 4. 2. ] B F is equal to B C. Therefore the gno- A H G K M N D mon KLM , and the fquare CF , are equal to twice the rectangle under the ...
Page 84
... double figure . Then because C B is equal to в D , but C B [ by 34. 1. ] is equal to G K , and BD to KN ; therefore GK will be And for the fame reafon alfo PR will be equal to K N. equal to R o . A M T G K X SP R ΣΚ E T H L F And ...
... double figure . Then because C B is equal to в D , but C B [ by 34. 1. ] is equal to G K , and BD to KN ; therefore GK will be And for the fame reafon alfo PR will be equal to K N. equal to R o . A M T G K X SP R ΣΚ E T H L F And ...
Page 85
... double to the fquares of half the line , and of the right line between the points of division & . For let any right line A B be divided into equal parts at c , and into unequal ones at D : I fay , the fquares of A D , DB are double to ...
... double to the fquares of half the line , and of the right line between the points of division & . For let any right line A B be divided into equal parts at c , and into unequal ones at D : I fay , the fquares of A D , DB are double to ...
Page 86
... double to the fquare of G F. But [ by 34. 1. ] F G is equal to CD : therefore the fquare of E F will be double to the fquare of c D. But alfo the fquare of A E is double to the fquare of AC ; therefore the fquares of A E , E F are double ...
... double to the fquare of G F. But [ by 34. 1. ] F G is equal to CD : therefore the fquare of E F will be double to the fquare of c D. But alfo the fquare of A E is double to the fquare of AC ; therefore the fquares of A E , E F are double ...
Page 87
... double to the fquares of A C , CD . But D F is equal to DB ; therefore the fquares of A D , DB will be double to the fquares of A C , C D. If therefore a right line be divided into two equal and into two unequal parts , the fquares of ...
... double to the fquares of A C , CD . But D F is equal to DB ; therefore the fquares of A D , DB will be double to the fquares of A C , C D. If therefore a right line be divided into two equal and into two unequal parts , the fquares of ...
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...