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 10
Side 273
... therefore the circle ABCD is not to the circle EFGH , as the cone AL is to any
solid greater than the cone EN : and it has been demonstrated that neither is the
circle ABCD to the circle EFGH , as the cone AL to any solid less than the cone
EN ...
... therefore the circle ABCD is not to the circle EFGH , as the cone AL is to any
solid greater than the cone EN : and it has been demonstrated that neither is the
circle ABCD to the circle EFGH , as the cone AL to any solid less than the cone
EN ...
Side 313
this book : the author of it designed to demonstrate , that if four magnitudes E , G ,
F , H be proportionals , they are also ... its demonstration : for , when he says , “
because it is demonstrated that if K be greater than M , L is greater than N , ” & c .
this book : the author of it designed to demonstrate , that if four magnitudes E , G ,
F , H be proportionals , they are also ... its demonstration : for , when he says , “
because it is demonstrated that if K be greater than M , L is greater than N , ” & c .
Side 318
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 320
B. V. The demonstration of this is none of Euclid's , nor is it legi . timate ; for it
depends upon this hypothesis , that to any ... be demonstrated by the
propositions preceding this : so far is it from deserving to be reckoned an axiom ,
as Clavius ...
B. V. The demonstration of this is none of Euclid's , nor is it legi . timate ; for it
depends upon this hypothesis , that to any ... be demonstrated by the
propositions preceding this : so far is it from deserving to be reckoned an axiom ,
as Clavius ...
Side 325
To this a case is added which occurs not unfrequently in demonstration . PROP .
VIII . B. VI . It seems plain that some editor has changed the demonstration that
Euclid gave of this proposition : for , after he has demonstrated , that the triangles
...
To this a case is added which occurs not unfrequently in demonstration . PROP .
VIII . B. VI . It seems plain that some editor has changed the demonstration that
Euclid gave of this proposition : for , after he has demonstrated , that the triangles
...
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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 |