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 63
... square of the fide fubtending the obtufe angle is greater than the fquares of the fides containing the obtufe angle , by twice the rectangle contained by the fide upon which , when produced , the perpendicular falls , and the straight ...
... square of the fide fubtending the obtufe angle is greater than the fquares of the fides containing the obtufe angle , by twice the rectangle contained by the fide upon which , when produced , the perpendicular falls , and the straight ...
Seite 64
... square of DC : To each of thefe equals add the fquare of AD ; therefore the fquares of CB , BD , DA are equal to twice the rectangle CB , BD , and the fquares of AD , DC : But the fquare of AB is equal D to the fquares of BD , DA ...
... square of DC : To each of thefe equals add the fquare of AD ; therefore the fquares of CB , BD , DA are equal to twice the rectangle CB , BD , and the fquares of AD , DC : But the fquare of AB is equal D to the fquares of BD , DA ...
Seite 65
... square that fhall be equal to a given see N ' rectilineal figure . Let A be the given rectilineal figure ; it is required to de- fcribe a fquare that fhall be equal to A. Defcribe the rectangular parallelogram BCDE equal to the a . 45 ...
... square that fhall be equal to a given see N ' rectilineal figure . Let A be the given rectilineal figure ; it is required to de- fcribe a fquare that fhall be equal to A. Defcribe the rectangular parallelogram BCDE equal to the a . 45 ...
Seite 66
... square of EG , is equal to the fquares of HE , EG : Take away the fquare of EG , which is common to both ; and the remaining rect- angle BE , EF is equal to the fquare of EH : But the rectangle contained by BE , EF is the parallelogram ...
... square of EG , is equal to the fquares of HE , EG : Take away the fquare of EG , which is common to both ; and the remaining rect- angle BE , EF is equal to the fquare of EH : But the rectangle contained by BE , EF is the parallelogram ...
Seite 80
... square of FE is equal to the remaining fquare of EG , and the straight line FE is therefore equal to EG : But ftraight lines in a circle are faid to be equally distant from the center , when the perpendiculars 4. Def . 3. drawn to them ...
... square of FE is equal to the remaining fquare of EG , and the straight line FE is therefore equal to EG : But ftraight lines in a circle are faid to be equally distant from the center , when the perpendiculars 4. Def . 3. drawn to them ...
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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
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.