The Elements of Euclid: The Errors by which Theon, Or Others, Have Long Vitiated These Books, are Corrected, and Some of Euclid's Demonstrations are Restored. Also the Book of Euclid's Data, in Like Manner Corrected. viz. the first six books, together with the eleventh and twelfth |
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Side 260
... to BC ; which was shewn to be impossible : therefore the sphere ABC has not
to any sphere greater than DEF the triplicate ratio of that which BC has to EF :
and it was demonstrated , that neither has it that ratio to any sphere less than
DEF .
... to BC ; which was shewn to be impossible : therefore the sphere ABC has not
to any sphere greater than DEF the triplicate ratio of that which BC has to EF :
and it was demonstrated , that neither has it that ratio to any sphere less than
DEF .
Side 288
Wherefore the 10th proposition is not sufficiently demonstrated . And it seems that
he who has given the demonstration of the 10th proposition as we now have it ,
instead of that which Eudoxus or Euclid had given , has been deceived in ...
Wherefore the 10th proposition is not sufficiently demonstrated . And it seems that
he who has given the demonstration of the 10th proposition as we now have it ,
instead of that which Eudoxus or Euclid had given , has been deceived in ...
Side 290
Euclid does not demonstrate it , nor does he show how to find the fourth
proportional , before the 12th Prop . of the 6th ... in the demonstration of a
proposition which he had not before demonstrated ; at least , he assumes nothing
the existence ...
Euclid does not demonstrate it , nor does he show how to find the fourth
proportional , before the 12th Prop . of the 6th ... in the demonstration of a
proposition which he had not before demonstrated ; at least , he assumes nothing
the existence ...
Side 293
... and published after his death , in the History of the Royal Academy of Sciences
of Berlin , anno 1745 , page 50 , the 23d prop . of the 5th book is censured as
being obscurely enunciated , and , because of this , prolixly demonstrated ...
... and published after his death , in the History of the Royal Academy of Sciences
of Berlin , anno 1745 , page 50 , the 23d prop . of the 5th book is censured as
being obscurely enunciated , and , because of this , prolixly demonstrated ...
Side 295
A ; viz . the case in which the exterior angle of a triangle is bisected by a straight
line : the demonstration of it is very like to ... demonstrated that the triangles are
equiangular to one another , he particularly shews that their sides about the
equal ...
A ; viz . the case in which the exterior angle of a triangle is bisected by a straight
line : the demonstration of it is very like to ... demonstrated that the triangles are
equiangular to one another , he particularly shews that their sides about the
equal ...
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The Elements of Euclid, Viz: The Errors, by which Theon, Or Others, Have ... Robert Simson Uten tilgangsbegrensning - 1775 |
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 Ago ... Robert Simson Uten tilgangsbegrensning - 1781 |
Vanlige uttrykk og setninger
added altitude angle ABC angle BAC base Book centre circle circle ABCD circumference common cone contained cylinder definition demonstrated described diameter difference divided double draw drawn equal equal angles equiangular equimultiples Euclid excess figure fore four fourth given angle given in position given in species given magnitude given ratio given straight line greater Greek half join less likewise logarithm magnitude manner meet multiple opposite parallel parallelogram pass perpendicular plane prism produced PROP proportionals proposition proved pyramid radius reason rectangle rectilineal figure remaining right angles segment shewn sides similar sine solid sphere square square of AC taken THEOR third triangle ABC wherefore whole
Populære avsnitt
Side 141 - 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 40 - If there be two straight lines, one of which is divided into any number of parts, the rectangle contained by the two straight lines is equal to the rectangles contained by the undivided line, and the several parts of the divided line. Let...
Side 26 - If a straight line fall upon two parallel straight lines, it makes the alternate angles equal to one another, and the exterior angle equal to the interior and opposite upon the same side, and also the two interior angles upon the same side together equal to two right angles.
Side 46 - If a straight line be divided into any two parts, four times the rectangle contained by the whole line and one of the parts, together with the square of the other part, is equal to the square of the straight line which is made up of the whole and that part.
Side 28 - Cor. angles; that is * together with four right angles. There1s, 1. fore 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 21 - If two triangles have two sides of the one equal to two sides of the other, each to each, but the angle contained by the two sides of one of them greater than the angle contained by the two sides equal to them, of the other ; the base of that which has the greater angle shall be greater than the base of the other.
Side 12 - IF two triangles have two sides of the one equal to two sides of the other, each to each, and have likewise their bases equal; the angle. which is contained by the two sides...
Side 169 - Wherefore, in equal circles &c. QED PROPOSITION B. THEOREM If the vertical angle of a triangle be bisected by a straight line which likewise cuts the base, the rectangle contained by the sides of the triangle is equal to the rectangle contained by the segments of the base, together with the square on the straight line which bisects the angle.
Side 5 - LET it be granted that a straight line may be drawn from any one point to any other point. 2. That a terminated straight line may be produced to any length in a straight line. 3. And that a circle may be described from any centre, at any distance from that centre.
Side 97 - 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.
Bibliografisk informasjon
| Tittel | The Elements of Euclid: The Errors by which Theon, Or Others, Have Long Vitiated These Books, are Corrected, and Some of Euclid's Demonstrations are Restored. Also the Book of Euclid's Data, in Like Manner Corrected. viz. the first six books, together with the eleventh and twelfth |
| Forfatter | Robert Simson |
| Redaktør | Richard Newton Adams |
| oversatt av | Abram Robertson |
| Utgiver | J. Collingwood, 1827 |
| Original fra | University of Michigan |
| Digitalisert | 11. jun 2007 |
| Lengde | 513 sider |
| Eksporter sitat | BiBTeX EndNote RefMan |