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 105
wherefore the circle described from the centre F , at the distance of one of them ,
shall pass through the extremities of the other two , and be described about the
triangle ABC . Which was to be done . COR . And it is manifest , that when the ...
wherefore the circle described from the centre F , at the distance of one of them ,
shall pass through the extremities of the other two , and be described about the
triangle ABC . Which was to be done . COR . And it is manifest , that when the ...
Side 252
For , if it be not so , the square of BD shall be to the square of FH , as the circle
ABCD is to some space either less than the circle EFGH , or greater than it . †
First let it be to a space S less than the circle EFGH ; and in the circle EFGH
describe ...
For , if it be not so , the square of BD shall be to the square of FH , as the circle
ABCD is to some space either less than the circle EFGH , or greater than it . †
First let it be to a space S less than the circle EFGH ; and in the circle EFGH
describe ...
Side 254
space S : therefore as the circle ABCD is to the space S , so is ( 11.5 . ) the
polygon AXBOCPDR to the polygon EKFLGMHN : but the circle ABCD is greater
than the polygon contained in it : wherefore the space S is greater ( 14. 5. ) than
the ...
space S : therefore as the circle ABCD is to the space S , so is ( 11.5 . ) the
polygon AXBOCPDR to the polygon EKFLGMHN : but the circle ABCD is greater
than the polygon contained in it : wherefore the space S is greater ( 14. 5. ) than
the ...
Side 255
square of FH is to the square of BD , so is the circle EFGH to a space less than
the circle ABCD , which has been demonstrated to be impossible : therefore the
square of BD is not to the square of FH , as the circle ABCD is to any space
greater ...
square of FH is to the square of BD , so is the circle EFGH to a space less than
the circle ABCD , which has been demonstrated to be impossible : therefore the
square of BD is not to the square of FH , as the circle ABCD is to any space
greater ...
Side 273
than the pyramid in the cone EN ; but it is less , as was shown , which is absurd :
therefore the circle ABCD is not to the circle EFGH , as the cone AL to any solid
which is less than the cone EN . In the same manner it may be denionstrated that
...
than the pyramid in the cone EN ; but it is less , as was shown , which is absurd :
therefore the circle ABCD is not to the circle EFGH , as the cone AL to any solid
which is less than the cone EN . In the same manner it may be denionstrated that
...
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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 |