Euclid's Elements of Geometry: The First Six, the Eleventh and Twelfth Books |
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Page 124
... touch another outwardly in more points than one . For if poffible , let the circle ACK touch the circle ABDC outwardly in more points than one , viz . in A , C , and draw A C. Then because two points A , C , are taken in the circum ...
... touch another outwardly in more points than one . For if poffible , let the circle ACK touch the circle ABDC outwardly in more points than one , viz . in A , C , and draw A C. Then because two points A , C , are taken in the circum ...
Page 128
... touch a given circle h . Let the given point be A , and the given circle be BC D. It is required to draw a right line from the point A , to touch the circle C D. For find the centre E of the circle ; join A E , and about the centre E ...
... touch a given circle h . Let the given point be A , and the given circle be BC D. It is required to draw a right line from the point A , to touch the circle C D. For find the centre E of the circle ; join A E , and about the centre E ...
Page 129
... touch the circle A B C. C D E B For because E is the centre of the circles B CD , AFG ; EA will be equal to E F , and ED equal to E B : Wherefore the two fides A E , E B are equal to the two fides FE , ED , and they contain the common ...
... touch the circle A B C. C D E B For because E is the centre of the circles B CD , AFG ; EA will be equal to E F , and ED equal to E B : Wherefore the two fides A E , E B are equal to the two fides FE , ED , and they contain the common ...
Page 130
... touch the circle A B C in the point . c , and from the centre F of the circle A B C let the right line C F be drawn to c : I fay , CF is perpendicular to DE . For if it be not , draw [ by 12. 1. ] F G from F perpen- dicular to DE . Then ...
... touch the circle A B C in the point . c , and from the centre F of the circle A B C let the right line C F be drawn to c : I fay , CF is perpendicular to DE . For if it be not , draw [ by 12. 1. ] F G from F perpen- dicular to DE . Then ...
Page 141
... touch the circle A B CD in B , and draw any right line BD from B cutting the circle : I fay , the angles that BD makes with the tangent E F , are equal to the angles which ftand in the alternate fegments of the circle ; that is , the ...
... touch the circle A B CD in B , and draw any right line BD from B cutting the circle : I fay , the angles that BD makes with the tangent E F , are equal to the angles which ftand in the alternate fegments of the circle ; that is , 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...