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 6
Side 57
If a straight line be divided into two equal , and also into two unequal parts ; the
squares of the two unequal parts are together double of the square of half the line
, and of the square of the line between the points of section . Let the straight line ...
If a straight line be divided into two equal , and also into two unequal parts ; the
squares of the two unequal parts are together double of the square of half the line
, and of the square of the line between the points of section . Let the straight line ...
Side 472
ML is to LG , as BC together with CD is to BD ; and , by composition , ML and LG
together , that is , producing GL to N , so that ML be equal to LN , the straight line
NG is to GL , as twice BC is to BD ; and by taking GO equal to the half of NG , GO
...
ML is to LG , as BC together with CD is to BD ; and , by composition , ML and LG
together , that is , producing GL to N , so that ML be equal to LN , the straight line
NG is to GL , as twice BC is to BD ; and by taking GO equal to the half of NG , GO
...
Side 483
S. In a plane triangle , the sum of any two sides is to their difference , as the
tangent of half the sum of the angles at the base , to the tangent of half their
difference . Let ABC be a plane triangle ; the sum of any two sides , AB , AC will
be to their ...
S. In a plane triangle , the sum of any two sides is to their difference , as the
tangent of half the sum of the angles at the base , to the tangent of half their
difference . Let ABC be a plane triangle ; the sum of any two sides , AB , AC will
be to their ...
Side 487
Half the given sum added to half the given difference , will be the greater , and
half the difference subtracted from half the sum , will be the less . For , let AB be
the given sum , AC the greater , and BC the less . Let AD be half the given sum ;
and ...
Half the given sum added to half the given difference , will be the greater , and
half the difference subtracted from half the sum , will be the less . For , let AB be
the given sum , AC the greater , and BC the less . Let AD be half the given sum ;
and ...
Side 512
The rectangle contained by half of the radius , and the excess of the versed sines
of two arches , is equal to the rectangle contained by the sines of half the sum ,
and half the difference of the same arches .. Let AB , AC be any two arches , and
...
The rectangle contained by half of the radius , and the excess of the versed sines
of two arches , is equal to the rectangle contained by the sines of half the sum ,
and half the difference of the same arches .. Let AB , AC be any two arches , and
...
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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 |