Elements of Geometry: Containing the First Six Books of Euclid, with a Supplement of the Quadrature of the Circle and the Geometry of Solids |
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Side 130
Thus , 3A signifies three times A ; mB , m times B , or a multiple of B by m . When
the number is intended to multiply two or more magnitudes that follow , it is
written thus , m.A + B , which signifies the sum of A and B taken m times ; ñ.A - B
is m ...
Thus , 3A signifies three times A ; mB , m times B , or a multiple of B by m . When
the number is intended to multiply two or more magnitudes that follow , it is
written thus , m.A + B , which signifies the sum of A and B taken m times ; ñ.A - B
is m ...
Side 131
See N. soever be taken of the first and third , and any equimultiples whatsoever
of the second and fourth , and if , according as the multiple of the first is greater
than the multiple of the second , equal to it , or less , the multiple of the third is
also ...
See N. soever be taken of the first and third , and any equimultiples whatsoever
of the second and fourth , and if , according as the multiple of the first is greater
than the multiple of the second , equal to it , or less , the multiple of the third is
also ...
Side 135
A multiple of a greater magnitude is greater than the same multiple of a less . IV .
That magnitude of which a multiple is greater than the same multiple of another ,
is greater than that other magnitude . Book V. PROP . I. THEOR . IF any number ...
A multiple of a greater magnitude is greater than the same multiple of a less . IV .
That magnitude of which a multiple is greater than the same multiple of another ,
is greater than that other magnitude . Book V. PROP . I. THEOR . IF any number ...
Side 136
Book V. PROP . I. THEOR . IF any number of magnitudes be equimultiples of as
many others , each of each , what multiple soever any one of the first is of its part ,
the same multiple is the sum of all the first of the sum of all the rest . a Ax 2. 1 .
Book V. PROP . I. THEOR . IF any number of magnitudes be equimultiples of as
many others , each of each , what multiple soever any one of the first is of its part ,
the same multiple is the sum of all the first of the sum of all the rest . a Ax 2. 1 .
Side 137
Therefore , if equals be added to equals , Book V. A + B is equal to C taken mtn
times ; that is , A + B = m + n.c . Therefore A + B contains C as often as there are
units in m + n . Q. E. D. Cor . 1. If there be any number of multiples whatever , as A
...
Therefore , if equals be added to equals , Book V. A + B is equal to C taken mtn
times ; that is , A + B = m + n.c . Therefore A + B contains C as often as there are
units in m + n . Q. E. D. Cor . 1. If there be any number of multiples whatever , as A
...
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Vanlige uttrykk og setninger
ABC is equal ABCD altitude angle ABC angle ACB angle BAC arch base bisected Book centre circle circle ABC circumference coincide common compounded contained cylinder definition demonstrated described diameter difference divided double draw drawn equal equal angles equiangular equilateral equimultiples exterior angle extremities fall figure fore fourth given straight line greater half inscribed interior join less Let ABC magnitudes manner meet multiple opposite parallel parallelogram pass perpendicular plane polygon prism PROB produced proportional proposition proved pyramid Q. E. D. PROP ratio reason rectangle contained rectilineal figure right angles segment shown sides similar solid space square taken THEOR third triangle ABC wherefore whole
Populære avsnitt
Side 121 - If two triangles have two angles of the one equal to two angles of the other, each to each, and one side equal to one side, viz. either the sides adjacent to the equal...
Side 42 - TO a given straight line to apply a parallelogram, which shall be equal to a given triangle, and have one of its angles equal to a given rectilineal angle.
Side 63 - Therefore, in obtuse-angled triangles, &c. QED PROP. XIII. THEOREM. In every triangle, the square of the side subtending either of the acute angles is less than the squares of the sides containing that angle, by twice the rectangle contained by either of these sides, and the straight line intercepted between the perpendicular let fall upon it from the opposite angle, and the acute angle.
Side 3 - A circle is a plane figure contained by one line, which is called the circumference, and is such that all straight lines drawn from a certain point within the figure to the circumference, are equal to one another.
Side 183 - Equiangular parallelograms have to one another the ratio which is compounded of the ratios of their sides. Let AC, CF be equiangular parallelograms having the angle BCD equal to the angle ECG ; the ratio of the parallelogram AC to the parallelogram CF is the same with the ratio which is compounded •f the ratios of their sides.
Side 3 - A diameter of a circle is a straight line drawn through the centre, and terminated both ways by the circumference.
Side 291 - 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 160 - ... extremities of the base shall have the same ratio which the other sides of the triangle have to one...
Side 10 - ... shall be greater than the base of the other. Let ABC, DEF be two triangles, which have the two sides AB, AC, equal to the two DE, DF, each to each, viz.
Side 14 - Therefore, upon the same base, and on the same side of it, there cannot be two triangles that have their sides which are terminated in one extremity of the base equal to one another, and likewise those which are terminated in the other extretnity equal to one another.
Bibliografisk informasjon
| Tittel | Elements of Geometry: Containing the First Six Books of Euclid, with a Supplement of the Quadrature of the Circle and the Geometry of Solids |
| Forfatter | John Playfair |
| Utgiver | F. Nichols, 1806 |
| Original fra | University of Michigan |
| Digitalisert | 16. feb 2008 |
| ISBN | 0608378402, 9780608378404 |
| Lengde | 311 sider |
| Eksporter sitat | BiBTeX EndNote RefMan |