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 σελίδες |
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Σελίδα 119
... second , which the third has to the fourth , when any e- quimultiples whatsoever of the firft and third being taken , and any equimultiples whatsoever of the fecond and fourth ; if the multiple of the first be less than that of the ...
... second , which the third has to the fourth , when any e- quimultiples whatsoever of the firft and third being taken , and any equimultiples whatsoever of the fecond and fourth ; if the multiple of the first be less than that of the ...
Σελίδα 120
... second , and of the ratio which the second has to the third , and of the ratio which the third has to the fourth , and fo on unto the last magnitude . For example , If A , B , C , D be four magnitudes of the fame kind , the firft A is ...
... second , and of the ratio which the second has to the third , and of the ratio which the third has to the fourth , and fo on unto the last magnitude . For example , If A , B , C , D be four magnitudes of the fame kind , the firft A is ...
Σελίδα 121
... second to the fourth : As is fhewn in the 16th prop . of this 5th book . XIV . Invertendo , by inverfion : When there are four proportionals , and it is inferred , that the fecond is to the firft , as the fourth to the third . Prop . B ...
... second to the fourth : As is fhewn in the 16th prop . of this 5th book . XIV . Invertendo , by inverfion : When there are four proportionals , and it is inferred , that the fecond is to the firft , as the fourth to the third . Prop . B ...
Σελίδα 122
... second rank ; and as the second is to the third of the first rank , fo is the laft but two to the last but one of the second rank ; and as the third is to the fourth of the first rank , fo is the third from the last to the last but two ...
... second rank ; and as the second is to the third of the first rank , fo is the laft but two to the last but one of the second rank ; and as the third is to the fourth of the first rank , fo is the third from the last to the last but two ...
Σελίδα 125
... second , which the third is of the fourth ; and if of the first and third there be taken equimultiples , thefe fhall be equi- multiples the one of the fecond , and the other of the fourth . Let A the firft be the fame multiple of B the ...
... second , which the third is of the fourth ; and if of the first and third there be taken equimultiples , thefe fhall be equi- multiples the one of the fecond , and the other of the fourth . Let A the firft be the fame multiple of B the ...
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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
Δημοφιλή αποσπάσματα
Σελίδα 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...
Σελίδα 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.
Σελίδα 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.
Σελίδα 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...
Σελίδα 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.
Σελίδα 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.
Σελίδα 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.
Σελίδα 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.
Σελίδα 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.
Σελίδα 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.