Euclid's Elements of Geometry: The First Six, the Eleventh and Twelfth BooksJ. Rivington, 1765 - 464 sider |
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Side ix
... plane and folid geometry , as the first fix , eleventh , and twelfth books . Accordingly these eight books alone by most of the moderns have been looked upon as fuffici- ent Elements of that plane and folid geometry , in ufe and fashion ...
... plane and folid geometry , as the first fix , eleventh , and twelfth books . Accordingly these eight books alone by most of the moderns have been looked upon as fuffici- ent Elements of that plane and folid geometry , in ufe and fashion ...
Side 4
... plane , neither inclining nor reclining , but having all the perpendiculars equal , that are drawn from the points of either of the lines to the other line .--- Others call them equidifant right lines in one plane . --- Others fay ...
... plane , neither inclining nor reclining , but having all the perpendiculars equal , that are drawn from the points of either of the lines to the other line .--- Others call them equidifant right lines in one plane . --- Others fay ...
Side 5
... plane above , and the other in a plane bencath , may be in- finitely produced both ways , and never meet , and yet not be fuch as Euclid calls parallels . --- This eighth axiom is univerfally convertible , although Proclus , Borelius ...
... plane above , and the other in a plane bencath , may be in- finitely produced both ways , and never meet , and yet not be fuch as Euclid calls parallels . --- This eighth axiom is univerfally convertible , although Proclus , Borelius ...
Side 6
... plane , muft neceffarily meet or be parallel ; and if they meet , it B muft either be to the right or left of the right line E F falling upon D them , what man of common fenfe would fay they would meet to the left ? If both the angles E ...
... plane , muft neceffarily meet or be parallel ; and if they meet , it B muft either be to the right or left of the right line E F falling upon D them , what man of common fenfe would fay they would meet to the left ? If both the angles E ...
Side 219
... are applicable to all magnitudes in general , lines , planes , folids , commenfurable , and incommenfurable , Euclid could not but demonftrate them . PROP . PROP . VIII , THEOR . The greater of [ Book V , 219 Euclid's Elements .
... are applicable to all magnitudes in general , lines , planes , folids , commenfurable , and incommenfurable , Euclid could not but demonftrate them . PROP . PROP . VIII , THEOR . The greater of [ Book V , 219 Euclid's Elements .
Andre udgaver - Se alle
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...