Euclid's Elements of Geometry: The First Six, the Eleventh and Twelfth BooksJ. Rivington, 1765 - 464 sider |
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Resultat 1-5 av 100
Side x
... whole more compleat elements of common geometry and fome of thefe are new , at least to me ; fuch as Prop . ii . at page 54 . Prop . vii . at page 64. the Scholium at page 97. the Scholium at page 100. Prop . viii . at page 204 . Prop ...
... whole more compleat elements of common geometry and fome of thefe are new , at least to me ; fuch as Prop . ii . at page 54 . Prop . vii . at page 64. the Scholium at page 97. the Scholium at page 100. Prop . viii . at page 204 . Prop ...
Side xiii
... whole Doc- trine of the Proportionality of Magnitudes con- tained in the Fifth Book , may be clearly , briefly , and easily , ftated and demonftrated , whether the Magnitudes be commenfurable or incommenfurable , by a clear Definition ...
... whole Doc- trine of the Proportionality of Magnitudes con- tained in the Fifth Book , may be clearly , briefly , and easily , ftated and demonftrated , whether the Magnitudes be commenfurable or incommenfurable , by a clear Definition ...
Side 5
... whole is greater than a part of it . IO . * All right angles are equal to one another . II . If a right line falling upon two right lines does make the internal angles on the fame fide lefs than two right an- one plane above , and the ...
... whole is greater than a part of it . IO . * All right angles are equal to one another . II . If a right line falling upon two right lines does make the internal angles on the fame fide lefs than two right an- one plane above , and the ...
Side 10
... whole triangle ABC agrees with the whole triangle DEF , and will be equal to the fame ; and the remaining angles will agree with the remaining an- gles , and therefore fhall be equal to them , viz . the angle ABC to the angle DEF , and ...
... whole triangle ABC agrees with the whole triangle DEF , and will be equal to the fame ; and the remaining angles will agree with the remaining an- gles , and therefore fhall be equal to them , viz . the angle ABC to the angle DEF , and ...
Side 11
... whole line AF is equal to the whole line A G , and A B is equal to A C ; therefore the remainder BF will be equal to the remainder CG [ by ax . 3. ] But it has been proved , that the right line FC is equal to the right line G B ...
... whole line AF is equal to the whole line A G , and A B is equal to A C ; therefore the remainder BF will be equal to the remainder CG [ by ax . 3. ] But it has been proved , that the right line FC is equal to the right line G B ...
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...