Euclid's Elements of Geometry: The First Six, the Eleventh and Twelfth BooksJ. Rivington, 1765 - 464 páginas |
Dentro del libro
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Página xi
... Ratio , viz . that this Defi- nition does really extend to commenfurable Mag- nitudes only , and not to incommenfurable ones ; although it has been generally thought , by all the modern Writers I have ever seen , to take in both ...
... Ratio , viz . that this Defi- nition does really extend to commenfurable Mag- nitudes only , and not to incommenfurable ones ; although it has been generally thought , by all the modern Writers I have ever seen , to take in both ...
Página xii
... Ratio , or may be compared together according to Quan- tity , and the latter thofe that cannot be compared together according to Quantity , as not having a Ratio according to his Notion and the Meaning of the Word in his Third ...
... Ratio , or may be compared together according to Quan- tity , and the latter thofe that cannot be compared together according to Quantity , as not having a Ratio according to his Notion and the Meaning of the Word in his Third ...
Página 205
... Ratio , according to the etymology of the word , fignifies a judgment , account , or estimation of things known , from a comparison of them . And I think the common english word rate gives a good notion of its meaning . In every ratio ...
... Ratio , according to the etymology of the word , fignifies a judgment , account , or estimation of things known , from a comparison of them . And I think the common english word rate gives a good notion of its meaning . In every ratio ...
Página 206
... ratio to one another , which being multiplied can exceed each other c . 5. Four magnitudes are faid to be in the fame ratio , the first to the fecond , and the third to the fourth : When the equimultiples of the first and third compared ...
... ratio to one another , which being multiplied can exceed each other c . 5. Four magnitudes are faid to be in the fame ratio , the first to the fecond , and the third to the fourth : When the equimultiples of the first and third compared ...
Página 207
... ratio , are called proportionals . N. B. When four magnitudes are proportionals it is ufually expreffed by faying , the first is to the second , as the third to the fourth . 7. But Let there be four magnitudes A , B , C , D where the ...
... ratio , are called proportionals . N. B. When four magnitudes are proportionals it is ufually expreffed by faying , the first is to the second , as the third to the fourth . 7. But Let there be four magnitudes A , B , C , D where the ...
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...