Euclid's Elements of Geometry: The First Six, the Eleventh and Twelfth BooksJ. Rivington, 1765 - 464 sider |
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Side 109
... touch a circle , when meeting it and being produced does not cut it . 3. Circles are faid to touch one another , which meeting one another do not cut one another . 4. Right lines in a circle are faid to be equally diftant from the ...
... touch a circle , when meeting it and being produced does not cut it . 3. Circles are faid to touch one another , which meeting one another do not cut one another . 4. Right lines in a circle are faid to be equally diftant from the ...
Side 112
... touch two points A , B in the circumfe- rence of the circle A B , whofe centre is c : I fay , the right line AB falls within the circle , fo that all its intermediate points will be within the circle . For take any one of its intermedi ...
... touch two points A , B in the circumfe- rence of the circle A B , whofe centre is c : I fay , the right line AB falls within the circle , fo that all its intermediate points will be within the circle . For take any one of its intermedi ...
Side 115
... touch one D F EB another inwardly , they will not both have the fame centre . Which was to be demonftrated . f Euclid only propofed this theorem of circles touching one another inwardly ; for when they touch outwardly , it is most ...
... touch one D F EB another inwardly , they will not both have the fame centre . Which was to be demonftrated . f Euclid only propofed this theorem of circles touching one another inwardly ; for when they touch outwardly , it is most ...
Side 122
... touch one another inwardly , and their centres be taken , the right line joining their centres being produced , will fall in the point wherein those circles touch one another . For let two circles A B C , A D E , touch one another in ...
... touch one another inwardly , and their centres be taken , the right line joining their centres being produced , will fall in the point wherein those circles touch one another . For let two circles A B C , A D E , touch one another in ...
Side 123
... touch one another outwardly , the right line joining their centres will pass thro ' the point wherein the circles touch one another . B E For let two circles AB C , AD E , touch one another outwardly in the point A. Let F be the centre ...
... touch one another outwardly , the right line joining their centres will pass thro ' the point wherein the circles touch one another . B E For let two circles AB C , AD E , touch one another outwardly in the point A. Let F be the centre ...
Andre utgaver - Vis alle
Euclid's Elements of Geometry: The First Six, the Eleventh and Twelfth Books Euclid,David Gregory Ingen forhåndsvisning tilgjengelig - 2023 |
Euclid's Elements of Geometry: The First Six, the Eleventh and Twelfth Books Euclid,David Gregory Ingen forhåndsvisning tilgjengelig - 2023 |
Euclid's Elements of Geometry: The First Six, the Eleventh and Twelfth Books Euclid,David Gregory Ingen forhåndsvisning tilgjengelig - 2016 |
Vanlige uttrykk og setninger
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
Populære avsnitt
Side 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.
Side 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...
Side 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.
Side 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.
Side 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.
Side 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.
Side 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...
Side 110 - If any two points be taken in the circumference of a circle, the straight line which joins them shall fall within the circle.
Side 130 - When you have proved that the three angles of every triangle are equal to two right angles...
Side 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...