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 sider |
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Resultat 6-10 av 63
Side 79
... must be within the fame cir- cle , which is abfurd : Therefore one circle cannot touch another on the out- fide in more than one point .: And it has been fhewn , that they cannot touch K on the infide in more points than one : Therefore ...
... must be within the fame cir- cle , which is abfurd : Therefore one circle cannot touch another on the out- fide in more than one point .: And it has been fhewn , that they cannot touch K on the infide in more points than one : Therefore ...
Side 82
... must fall without the circle , as AE . C 12. 1 . d 19. I. F E C H A D And between the ftraight line AE and the circumference no ftraight line can be drawn from the point A which does not cut the circle : For , if poffible , let FA be ...
... must fall without the circle , as AE . C 12. 1 . d 19. I. F E C H A D And between the ftraight line AE and the circumference no ftraight line can be drawn from the point A which does not cut the circle : For , if poffible , let FA be ...
Side 93
... must be lefs than a right angle ; and there , fore the angle in a fegment ABC greater than a femicircle , is lefs than a right angle , And because ABCD is a quadrilateral figure in a circle , any two of its oppofite angles are equal to ...
... must be lefs than a right angle ; and there , fore the angle in a fegment ABC greater than a femicircle , is lefs than a right angle , And because ABCD is a quadrilateral figure in a circle , any two of its oppofite angles are equal to ...
Side 164
... must be greater than a right angle . 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 hypothefis , it is lefs than a right angle ; which is abfurd ...
... must be greater than a right angle . 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 hypothefis , it is lefs than a right angle ; which is abfurd ...
Side 182
... must be equal . It is required to defcribe a rectilineal figure fimilar to ABC and equal to D. Cor . 45.1 . Upon the straight line BC defcribe the parallelogram BE equal to the figure ABC ; also upon CE defcribe the paralle logram CM ...
... must be equal . It is required to defcribe a rectilineal figure fimilar to ABC and equal to D. Cor . 45.1 . Upon the straight line BC defcribe the parallelogram BE equal to the figure ABC ; also upon CE defcribe the paralle logram CM ...
Andre utgaver - Vis alle
The Elements of Euclid: The Errors, by which Theon, Or Others, Have Long Ago ... Robert Simson Uten tilgangsbegrensning - 1762 |
The Elements of Euclid: The Errors by which Theon, Or Others, Have Long ... Robert Simson Uten tilgangsbegrensning - 1827 |
The Elements of Euclid: The Errors, by which Theon, Or Others, Have Long Ago ... Robert Simson Uten tilgangsbegrensning - 1781 |
Vanlige uttrykk og setninger
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
Populære avsnitt
Side 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...
Side 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.
Side 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.
Side 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...
Side 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.
Side 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.
Side 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.
Side 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.
Side 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.
Side 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.