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 1-5 av 43
Side 70
... pass through the center , it shall cut it at right angles ; And if it cuts it at right angles , it shall bisect it . Let ABC be a circle ; and let CD , a straight line drawn through the center bisect any straight line AB , which does not ...
... pass through the center , it shall cut it at right angles ; And if it cuts it at right angles , it shall bisect it . Let ABC be a circle ; and let CD , a straight line drawn through the center bisect any straight line AB , which does not ...
Side 71
... pass through the center : AC , BD do not bisect one another . For , if it is possible , let AE be equal to EC , and BE to ED : If one of the lines pass thro ' the center , it is plain that it can- not be bisected by the other which ...
... pass through the center : AC , BD do not bisect one another . For , if it is possible , let AE be equal to EC , and BE to ED : If one of the lines pass thro ' the center , it is plain that it can- not be bisected by the other which ...
Side 73
... passes through the center is al- ways greater than one more remote : And from the fame point there can be drawn only two straight lines that are equal to one another , one upon each fide of the shorteft line . Let ABCD be a circle , and ...
... passes through the center is al- ways greater than one more remote : And from the fame point there can be drawn only two straight lines that are equal to one another , one upon each fide of the shorteft line . Let ABCD be a circle , and ...
Side 74
... passes through the center ; and of the rest , that which is nearer to that through the center is always greater than the more remote : But of those which fall upon the convex circumference , the least is that between the point without ...
... passes through the center ; and of the rest , that which is nearer to that through the center is always greater than the more remote : But of those which fall upon the convex circumference , the least is that between the point without ...
Side 77
... pass through it . Therefore , if two circles , & c . Q. E. D. PROP . XII . THEOR . IF two circles touch each other externally , the straight line which joins their centers shall pass through the point of contact .. Let the two circles ...
... pass through it . Therefore , if two circles , & c . Q. E. D. PROP . XII . THEOR . IF two circles touch each other externally , the straight line which joins their centers shall pass through the point of contact .. Let the two circles ...
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 becauſe the ratio biſected Book XI cafe cauſe circle ABCD circumference cone confequently conſtruction cylinder demonſtration deſcribed diameter drawn EFGH equal angles equiangular equimultiples Euclid exceſs fame multiple fame ratio fame reaſon fides fides BA fimilar firſt folid angle fore given angle given in magnitude given in poſition given in ſpecies given magnitude given ratio given ſtraight line gnomon greater join leſs line BC oppoſite parallel parallelepipeds parallelogram paſs perpendicular priſm proportionals propoſition pyramid Q. E. D. PROP rectangle contained rectilineal figure right angles ſame ſecond ſegment ſhall ſhewn ſide ſolid ſpace ſphere ſquare of AC THEOR theſe thoſe 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.