The Elements of Euclid, Viz: The Errors, by which Theon, Or Others, Have Long Ago Vitiated These Books, are Corrected; and Some of Euclid's Demonstrations are Restored. Also the Book of Euclid's Data, in Like Manner Corrected. the first six books, together with the eleventh and twelfthJ. Nourse, London, and J. Balfour, Edinburgh, 1775 - 520 Seiten |
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Seite 119
... Ratio is a mutual relation of two magnitudes of the fame See N • kind to one another , in refpect of quantity . ' IV . Magnitudes are said to have a ratio to one another , when the lefs can be multiplied fo as to exceed the other . V ...
... Ratio is a mutual relation of two magnitudes of the fame See N • kind to one another , in refpect of quantity . ' IV . Magnitudes are said to have a ratio to one another , when the lefs can be multiplied fo as to exceed the other . V ...
Seite 120
... fame ratio are called proportionals , N. B. When four magnitudes are proportionals , it is ufu- ally expreffed by faying , the first is to the fecond , as the third to the fourth . " VII . When of the equimultiples of four magnitudes ...
... fame ratio are called proportionals , N. B. When four magnitudes are proportionals , it is ufu- ally expreffed by faying , the first is to the fecond , as the third to the fourth . " VII . When of the equimultiples of four magnitudes ...
Seite 121
... fame ratio which E has to F ; and B Book V. to C , the fame ratio that G has to H ; and C to D , the fame that K has to L ; then , by this definition , A is faid to have to the ratio compounded of ratios which are the same with the ratios ...
... fame ratio which E has to F ; and B Book V. to C , the fame ratio that G has to H ; and C to D , the fame that K has to L ; then , by this definition , A is faid to have to the ratio compounded of ratios which are the same with the ratios ...
Seite 126
... fame ratio to the fecond which the third has to the fourth ; then any equimultiples whatever of the first and third fhall have the fame ratio to any equimultiples of the second and fourth , viz . the equimultiple of the firft fhall have ...
... fame ratio to the fecond which the third has to the fourth ; then any equimultiples whatever of the first and third fhall have the fame ratio to any equimultiples of the second and fourth , viz . the equimultiple of the firft fhall have ...
Seite 127
... fame ratio to the Book V. fecond and fourth : And in like manner , the first and the third have the fame ratio to any equimultiples whatever of the second and fourth . Let A the first have to B the fecond , the fame ratio which the ...
... fame ratio to the Book V. fecond and fourth : And in like manner , the first and the third have the fame ratio to any equimultiples whatever of the second and fourth . Let A the first have to B the fecond , the fame ratio which the ...
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Häufige Begriffe und Wortgruppen
alfo alſo angle ABC angle BAC bafe baſe BC is equal BC is given becauſe the angle bifected Book XI cafe circle ABCD circumference cone confequently cylinder defcribed demonftrated diameter drawn equal angles equiangular equimultiples Euclid excefs faid fame manner fame multiple fame ratio fame reafon fecond fegment fhall fhewn fide BC fimilar firft firſt folid angle fome fore fphere fquare of AC ftraight line AB given angle given ftraight line given in fpecies given in magnitude given in pofition given magnitude given ratio gnomon greater join lefs likewife line BC oppofite parallel parallelepipeds parallelogram perpendicular polygon prifm propofition proportionals pyramid Q. E. D. PROP rectangle contained rectilineal figure right angles thefe THEOR theſe triangle ABC vertex wherefore
Beliebte Passagen
Seite 32 - 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...
Seite 165 - D ; wherefore the remaining angle at C is equal to the remaining angle at F ; Therefore the triangle ABC is equiangular to the triangle DEF.
Seite 170 - 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.
Seite 10 - When several angles are at one point B, any ' one of them is expressed by three letters, of which ' the letter that is at the vertex of the angle, that is, at ' the point in which the straight lines that contain the ' angle meet one another, is put between the other two ' letters, and one of these two is...
Seite 55 - If a straight line be divided into two equal parts, and also into two unequal parts; the rectangle contained by the unequal parts, together with the square of the line between the points of section, is equal to the square of half the line.
Seite 32 - ... then shall the other sides be equal, each to each; and also the third angle of the one to the third angle of the other. Let ABC, DEF be two triangles which have the angles ABC, BCA equal to the angles DEF, EFD, viz.
Seite 45 - To describe a parallelogram that shall be equal to a given triangle, and have one of its angles equal to a given rectilineal angle.
Seite 211 - AB shall be at right angles to the plane CK. Let any plane DE pass through AB, and let CE be the common section of the planes DE, CK ; take any point F in CE, from which draw FG in the plane DE at right D angles to CE ; and because AB is , perpendicular to the plane CK, therefore it is also perpendicular to every straight line in that plane meeting it (3.
Seite 38 - F, which is the common vertex of the triangles ; that is, together with four right angles. 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.
Seite 304 - Thus, if B be the extremity of the line AB, or the common extremity of the two lines AB, KB, this extremity is called a point, and has no length : For if it have any, this length must either be part of the length of the line AB, or of the line KB.