The Elements of Euclid: Viz, the First Six Books, Together with the Eleventh and Twelfth ; 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 |
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Resultat 1-5 av 9
Side 52
to the angle ABD , because BA is equal to AD , being sides of a square ;
wherefore A C B the angle CGB is equal to the angle GBC ; and therefore the
side BC is equal G ( 6. 1. ) to the side CG : but CB is equal H K ( 34. 1. ) also to
GK , and CG ...
to the angle ABD , because BA is equal to AD , being sides of a square ;
wherefore A C B the angle CGB is equal to the angle GBC ; and therefore the
side BC is equal G ( 6. 1. ) to the side CG : but CB is equal H K ( 34. 1. ) also to
GK , and CG ...
Side 161
At the points D , F , in the straight line DF , make ( 23. 1. ) the angle FDG equal to
either of the angles BAC , EDF ; and the angle DFG equal to the angle A ACB ;
wherefore the remaining D angle at B is equal to the reG maining one at G ( 32. 1
. ) ...
At the points D , F , in the straight line DF , make ( 23. 1. ) the angle FDG equal to
either of the angles BAC , EDF ; and the angle DFG equal to the angle A ACB ;
wherefore the remaining D angle at B is equal to the reG maining one at G ( 32. 1
. ) ...
Side 273
Wherefore cones and cylinders of the same altitude are to one another as their
bases . Q. E. D. PROP . XII . THEOR . Similar cones and cylinders have to one
another the triplicate ratio of that which the diameters of their bases have . * Let
the ...
Wherefore cones and cylinders of the same altitude are to one another as their
bases . Q. E. D. PROP . XII . THEOR . Similar cones and cylinders have to one
another the triplicate ratio of that which the diameters of their bases have . * Let
the ...
Side 289
Wherefore the whole solid polyhedron in the greater sphere has to the whole
solid polyhedron in the other , the triplicate ratio of that which AB , the
semidiameter of the first , has to the semidiameter of the other ; that is , which the
diameter BD ...
Wherefore the whole solid polyhedron in the greater sphere has to the whole
solid polyhedron in the other , the triplicate ratio of that which AB , the
semidiameter of the first , has to the semidiameter of the other ; that is , which the
diameter BD ...
Side 313
... for this last is the conclusion of the proposition . Wherefore these words , “
because it is demonstrated , ” & c . are wholly foreign to his design ; and he
should have proved , that if K be greater than M , L is greater than N , from this ,
that E , G ...
... for this last is the conclusion of the proposition . Wherefore these words , “
because it is demonstrated , ” & c . are wholly foreign to his design ; and he
should have proved , that if K be greater than M , L is greater than N , from this ,
that E , G ...
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The Elements of Euclid: Viz. the First Six Books, Together with the Eleventh ... Euclid,Robert Simson Uten tilgangsbegrensning - 1825 |
The Elements of Euclid: The Errors, by which Theon, Or Others, Have Long Ago ... Euclid,Robert Simson Uten tilgangsbegrensning - 1838 |
Vanlige uttrykk og setninger
added altitude angle ABC angle BAC base centre circle circle ABCD circumference common cone cylinder definition demonstrated described diameter divided double draw drawn equal equal angles equiangular equimultiples Euclid excess fore four fourth given angle given in position given in species given magnitude given ratio given straight line greater Greek half join less likewise magnitude manner meet multiple Note opposite parallel parallelogram pass perpendicular plane prism produced PROP proportionals proposition pyramid Q. E. D. PROP radius reason rectangle rectangle contained rectilineal figure remaining right angles segment shown sides similar sine solid solid angle sphere square square of AC taken THEOR third triangle ABC wherefore whole
Populære avsnitt
Side 9 - Let it be granted that a straight line may be drawn from any one point to any other point.
Side 81 - The angles in the same segment of a circle are equal to one another.
Side 315 - Equiangular parallelograms have to one another the ratio which is compounded of the ratios of their sides.
Side 33 - All the interior angles of any rectilineal figure, together with four right angles, are equal to twice as many right angles as the figure has sides.
Side 49 - If a straight line be divided into any two parts, the rectangle contained by the whole and one of the parts, is equal to the rectangle contained by the two parts, together with the square of the aforesaid part.
Side 96 - If from any point without a circle two straight lines be drawn, one of which cuts the circle, and the other touches it ; the rectangle contained by the whole line which cuts the circle, and the part of it without the circle, shall be equal to the square of the line which touches it.
Side 155 - 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 22 - ANY two angles of a triangle are together less than two right angles.
Side 25 - Let A, B, C be the three given straight lines, of which any two whatever are greater than the third, viz.
Side 24 - Any two sides of a triangle are together greater than the third side.
Bibliografisk informasjon
| Tittel | The Elements of Euclid: Viz, the First Six Books, Together with the Eleventh and Twelfth ; 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 |
| Forfattere | Euclid, Robert Simson |
| Utgiver | Desilver, 1829 |
| Original fra | University of Michigan |
| Digitalisert | 11. jun 2007 |
| Lengde | 516 sider |
| Eksporter sitat | BiBTeX EndNote RefMan |