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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Side 5
... given ; and by taking out of this Book , besides other things , the good Definition which Eudoxus or Euclid had given of Compound Ratio , and giving an absurd one in place of it in the 5th Definition of the 6th Book , which neither ...
... given ; and by taking out of this Book , besides other things , the good Definition which Eudoxus or Euclid had given of Compound Ratio , and giving an absurd one in place of it in the 5th Definition of the 6th Book , which neither ...
Side 175
... given straight line si- milar to one given , and fo on . Which was to be done . ' d 22. S. S PROP . ΧΙΧ . THEOR . IMILAR triangles are to one another in the duplicate ratio of their homologous fides . Let ABC , DEF be similar triangles ...
... given straight line si- milar to one given , and fo on . Which was to be done . ' d 22. S. S PROP . ΧΙΧ . THEOR . IMILAR triangles are to one another in the duplicate ratio of their homologous fides . Let ABC , DEF be similar triangles ...
Side 313
... proportion of numbers to one another is defined , " and treated of , yet without giving any definition of the ratio " of numbers ; tho ' fuch a definition was as neceffary and use- " ful to be given in that book , as in this : But ...
... proportion of numbers to one another is defined , " and treated of , yet without giving any definition of the ratio " of numbers ; tho ' fuch a definition was as neceffary and use- " ful to be given in that book , as in this : But ...
Side 320
... ratio to C , than B has to C , there muft , by the 7th def . of Book 5. be certain equimultiples of A and B , and ... given the demonstration of the roth propofition as we now have it , instead of that which Eudoxus or Euclid had given ...
... ratio to C , than B has to C , there muft , by the 7th def . of Book 5. be certain equimultiples of A and B , and ... given the demonstration of the roth propofition as we now have it , instead of that which Eudoxus or Euclid had given ...
Side 329
... ratio might have been made after the fame manner in which the definitions of duplicate and triplicate ratio are given , viz . " That as in several magni- " tudes that are continual proportionals , Euclid named the " ratio of the first ...
... ratio might have been made after the fame manner in which the definitions of duplicate and triplicate ratio are given , viz . " That as in several magni- " tudes that are continual proportionals , Euclid named the " ratio of the first ...
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.