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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Side vi
Also the Note on the 29th Proposition, Book 1st, is altered, and made more
explicit, and a more general Demonstration is given, instead of that which was in
the Note on the 10th Definition of Book 11th ; besides, the Translation is much ...
Also the Note on the 29th Proposition, Book 1st, is altered, and made more
explicit, and a more general Demonstration is given, instead of that which was in
the Note on the 10th Definition of Book 11th ; besides, the Translation is much ...
Side 296
And in this manner the definitions of a point , line , and superficies , are to be
understood . B. DEF . VII . B. I. Instead of this definition as it is in the Greek copies
, a more distinct one is given from a property of a plane superficies , which is ...
And in this manner the definitions of a point , line , and superficies , are to be
understood . B. DEF . VII . B. I. Instead of this definition as it is in the Greek copies
, a more distinct one is given from a property of a plane superficies , which is ...
Side 297
B. I. The words , “ which also divides the circle into two equal parts , " are added
at the end of this definition in all the copies , but are now left out as not belonging
to the definition , being only a corollary from it . Proclus demonstrates it by ...
B. I. The words , “ which also divides the circle into two equal parts , " are added
at the end of this definition in all the copies , but are now left out as not belonging
to the definition , being only a corollary from it . Proclus demonstrates it by ...
Side 311
To this citation from Dr. Barrow I have nothing to add , except that I fully believe
the 3d and 8th definitions are not ... B. V. It was necessary to add the word “
continual ” before " proportionals ” in this definition ; and thus it is cited in the 33d
prop ...
To this citation from Dr. Barrow I have nothing to add , except that I fully believe
the 3d and 8th definitions are not ... B. V. It was necessary to add the word “
continual ” before " proportionals ” in this definition ; and thus it is cited in the 33d
prop ...
Side 326
Theon's definition is this : a ratio is said to be compounded of ratios οταν αι των
λογων πηλικοτητες εφ ' εαυτας πολλαπλα . ... Dr. Gregory renders the last words
of the definition by illius facit quantitatem , ” makes the quantity of that ratio ; but in
...
Theon's definition is this : a ratio is said to be compounded of ratios οταν αι των
λογων πηλικοτητες εφ ' εαυτας πολλαπλα . ... Dr. Gregory renders the last words
of the definition by illius facit quantitatem , ” makes the quantity of that ratio ; but in
...
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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 |