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 7
Side 239
In this case likewise , if the solids AB , CD be equal , their bases are reciprocally
proportional to their altitudes , viz . the base EH to the base NP , as the altitude of
the solid CD to the altitude of the solid AB . Because the solid AB is equal to the ...
In this case likewise , if the solids AB , CD be equal , their bases are reciprocally
proportional to their altitudes , viz . the base EH to the base NP , as the altitude of
the solid CD to the altitude of the solid AB . Because the solid AB is equal to the ...
Side 266
The bases and altitudes of equal pyramids having triangular bases are
reciprocally proportional : and triangular pyramids ... DEFH are reciprocally
proportional , viz . the base ABC is to the base DEF , as the altitude of the
pyramid DEFH to the ...
The bases and altitudes of equal pyramids having triangular bases are
reciprocally proportional : and triangular pyramids ... DEFH are reciprocally
proportional , viz . the base ABC is to the base DEF , as the altitude of the
pyramid DEFH to the ...
Side 267
altitude of the pyramid ABCG : therefore , as the base ABC to the base DEF , so is
the altitude of the pyramid DEFH to the altitude of the pyramid ABCG : wherefore
the bases and altitudes of the pyramids ABCG , DEFH are reciprocally ...
altitude of the pyramid ABCG : therefore , as the base ABC to the base DEF , so is
the altitude of the pyramid DEFH to the altitude of the pyramid ABCG : wherefore
the bases and altitudes of the pyramids ABCG , DEFH are reciprocally ...
Side 273
Therefore , as the circle ABCD to the circle EFGH , so are the cylinders upon
them of the same altitude . Wherefore cones and cylinders of the same altitude
are to one another as their bases . Q. E. D. PROP . XII . THEOR . Similar cones
and ...
Therefore , as the circle ABCD to the circle EFGH , so are the cylinders upon
them of the same altitude . Wherefore cones and cylinders of the same altitude
are to one another as their bases . Q. E. D. PROP . XII . THEOR . Similar cones
and ...
Side 280
The bases and altitudes of equal cones and cylinders are reciprocally
proportional ; and , if the bases and altitudes be ... EO are reciprocally
proportional ; that is , as the base ABCD to the base EFGH , so is the altitude MN
to the altitude KL .
The bases and altitudes of equal cones and cylinders are reciprocally
proportional ; and , if the bases and altitudes be ... EO are reciprocally
proportional ; that is , as the base ABCD to the base EFGH , so is the altitude MN
to the altitude KL .
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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 |