Euclid's Elements of Geometry: The First Six, the Eleventh and Twelfth BooksJ. Rivington, 1765 - 464 páginas |
Dentro del libro
Resultados 6-10 de 17
Página 265
... Similar polygons are divided into equal numbers of fimilar triangles homologous to the wholes ; and one polygon has to another polygon a duplicate ratio to that which one homologous fide of the one bas to an homologous fide of the other ...
... Similar polygons are divided into equal numbers of fimilar triangles homologous to the wholes ; and one polygon has to another polygon a duplicate ratio to that which one homologous fide of the one bas to an homologous fide of the other ...
Página 269
... Similar and alike fituate be proportional ; thofe right lines will be proportionali . Let the four right lines A B , CD , EF , GH be propor tional , viz . as AB is to CD , fo is EF to GH ; and upon AB , CD , let the right lined figures ...
... Similar and alike fituate be proportional ; thofe right lines will be proportionali . Let the four right lines A B , CD , EF , GH be propor tional , viz . as AB is to CD , fo is EF to GH ; and upon AB , CD , let the right lined figures ...
Página 312
... Similar 9. Similar folid figures are thofe which are contained under [ 312 ] EUCLID's ...
... Similar 9. Similar folid figures are thofe which are contained under [ 312 ] EUCLID's ...
Página 313
The First Six, the Eleventh and Twelfth Books Euclid. 9. Similar folid figures are thofe which are contained under equal numbers of fimilar planes . 10. Equal and fimilar folid figures are fuch as are con- tained under fimilar planes ...
The First Six, the Eleventh and Twelfth Books Euclid. 9. Similar folid figures are thofe which are contained under equal numbers of fimilar planes . 10. Equal and fimilar folid figures are fuch as are con- tained under fimilar planes ...
Página 314
... Similar cones , and cylinders are those whose axes and the diameters of their bafes are proportional . e This definition of a cone is too fcanty , it only taking in a right cone , viz . that whofe axis is at right angles to the plane of ...
... Similar cones , and cylinders are those whose axes and the diameters of their bafes are proportional . e This definition of a cone is too fcanty , it only taking in a right cone , viz . that whofe axis is at right angles to the plane of ...
Otras ediciones - Ver todas
Euclid's Elements of Geometry: The First Six, the Eleventh and Twelfth Books Euclid,David Gregory Sin vista previa disponible - 2023 |
Euclid's Elements of Geometry: The First Six, the Eleventh and Twelfth Books Euclid,David Gregory Sin vista previa disponible - 2023 |
Euclid's Elements of Geometry: The First Six, the Eleventh and Twelfth Books Euclid,David Gregory Sin vista previa disponible - 2016 |
Términos y frases comunes
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
Pasajes populares
Página 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.
Página 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...
Página 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.
Página 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.
Página 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.
Página 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.
Página 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...
Página 110 - If any two points be taken in the circumference of a circle, the straight line which joins them shall fall within the circle.
Página 130 - When you have proved that the three angles of every triangle are equal to two right angles...
Página 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...