Euclid's Elements of Geometry: The First Six, the Eleventh and Twelfth BooksJ. Rivington, 1765 - 464 sider |
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Side 20
... manner , that no right line but B D can have the fame direction with the right line C B. Wherefore BC and B D lie both in the fame right line . It If therefore at a point in any right line , If 20 Book I. Euclid's Elements . If ...
... manner , that no right line but B D can have the fame direction with the right line C B. Wherefore BC and B D lie both in the fame right line . It If therefore at a point in any right line , If 20 Book I. Euclid's Elements . If ...
Side 21
... common angle A E D , then the remaining angle CEA is equal to the remaining angle B E D. In like manner it may be proved , that the angle C E B fhall C 3 be Book I. 21 Euclid's Elements . If therefore at a point in any right line, ...
... common angle A E D , then the remaining angle CEA is equal to the remaining angle B E D. In like manner it may be proved , that the angle C E B fhall C 3 be Book I. 21 Euclid's Elements . If therefore at a point in any right line, ...
Side 22
... manner , if B C be bifected , it will be demonftrated that the angle B C G , that is , [ by prop . 15. ] the angle A CD is greater than the angle A B C. ΒΕ is F G Therefore if any one fide of every triangle be produced , the the outward ...
... manner , if B C be bifected , it will be demonftrated that the angle B C G , that is , [ by prop . 15. ] the angle A CD is greater than the angle A B C. ΒΕ is F G Therefore if any one fide of every triangle be produced , the the outward ...
Side 25
... manner we demonstrate , that the fides A B , BC together , are greater than the fide C A , and the fides B C , CA together , greater than the fide A B. Therefore any two fides of every triangle , taken toge- ther , are greater than the ...
... manner we demonstrate , that the fides A B , BC together , are greater than the fide C A , and the fides B C , CA together , greater than the fide A B. Therefore any two fides of every triangle , taken toge- ther , are greater than the ...
Side 33
... 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 if a ...
... 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 if a ...
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Euclid's Elements of Geometry: The First Six, the Eleventh and Twelfth Books Euclid,David Gregory Ingen forhåndsvisning - 2023 |
Euclid's Elements of Geometry: The First Six, the Eleventh and Twelfth Books Euclid,David Gregory Ingen forhåndsvisning - 2023 |
Euclid's Elements of Geometry: The First Six, the Eleventh and Twelfth Books Euclid,David Gregory Ingen forhåndsvisning - 2016 |
Almindelige termer og sætninger
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 passager
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...