The Elements of Euclid: 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. viz. the first six books, together with the eleventh and twelfthMathew Carey, and sold by J. Conrad & Company, S. F. Bradford, Birch & Small, and Samuel Etheridge. Printed by T. & G. Palmer, 116, High-Street., 1806 - 518 Seiten |
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Seite 119
... and any equimultiples whatsoever of the second and fourth ; if the multiple of the first be less than that of the second , the multiple of the third is also less than that of the fourth ; or , if the multiple of the first be equal ...
... and any equimultiples whatsoever of the second and fourth ; if the multiple of the first be less than that of the second , the multiple of the third is also less than that of the fourth ; or , if the multiple of the first be equal ...
Seite 120
When of the equimultiples of four magnitudes ( taken as in the fifth definition ) the multiple of the first is greater than that of the second , but the multiple of the third is not greater than the multiple of the fourth ; then the ...
When of the equimultiples of four magnitudes ( taken as in the fifth definition ) the multiple of the first is greater than that of the second , but the multiple of the third is not greater than the multiple of the fourth ; then the ...
Seite 122
EQUIMULTIPLES of the same , or of equal magnitudes , are equal to one another . * 4 Prop . lib . 2. Archimedis de sphæra et cylindro , II . Book V. Those magnitudes of which the same 122 THE ELEMENTS.
EQUIMULTIPLES of the same , or of equal magnitudes , are equal to one another . * 4 Prop . lib . 2. Archimedis de sphæra et cylindro , II . Book V. Those magnitudes of which the same 122 THE ELEMENTS.
Seite 123
Book V. Those magnitudes of which the same , or equal magnitudes , are equimultiples , are equal to one another . III . A multiple of a greater magnitude is greater than the same · multiple of a less . a IV . That magnitude of which a ...
Book V. Those magnitudes of which the same , or equal magnitudes , are equimultiples , are equal to one another . III . A multiple of a greater magnitude is greater than the same · multiple of a less . a IV . That magnitude of which a ...
Seite 125
IF the first be the same multiple of the second , which the third is of the fourth ; and if of the first and third there be taken equimultiples , these shall be equimultiples , the one of the second , and the other of the fourth .
IF the first be the same multiple of the second , which the third is of the fourth ; and if of the first and third there be taken equimultiples , these shall be equimultiples , the one of the second , and the other of the fourth .
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Häufige Begriffe und Wortgruppen
ABCD added altitude angle ABC angle BAC base Book centre circle circle ABC circumference common cone cylinder definition demonstrated described diameter divided double draw drawn equal equal angles equiangular equimultiples 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 opposite parallel parallelogram pass perpendicular plane prisms produced PROP proportionals proposition pyramid 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
Beliebte Passagen
Seite 30 - Any two sides of a triangle are together greater than the third side.
Seite 64 - To divide a given straight line into two parts, so that the rectangle contained by the whole, and one of the parts, may be equal to the square of the other part.
Seite 30 - IF, from the ends of the side of a triangle, there be drawn two straight lines to a point within the triangle, these shall be less than the other two sides of the triangle, but shall contain a greater angle. Let...
Seite 59 - PROP. VIII. THEOR. IF a straight line be divided into any two parts, tour times the rectangle contained by the whole line, and one of the parts, together with the square of the other part, is equal to the square of the straight line which is made up of the whole and that part.
Seite 28 - If one side of a triangle be produced, the exterior angle is greater than either of the interior opposite angles.
Seite 165 - 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.
Seite 19 - THE angles at the base of an isosceles triangle are equal to one another : and, if the equal sides be produced, the angles upon the other side of the base shall be equal.
Seite 191 - In right angled triangles, the rectilineal figure described upon the side opposite to the right angle, is equal to the similar, and similarly described figures upon the sides containing the right angle.
Seite 39 - 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 sidef. For any rectilineal figure ABCDE can be divided into as many triangles as the figure has sides, by drawing straight lines from a point F within the figure to each of its angles.
Seite 180 - Therefore, universally, similar rectilineal figures are to one another in the duplicate ratio of their homologous sides.
Bibliografische Informationen
| Titel | The Elements of Euclid: 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. viz. the first six books, together with the eleventh and twelfth |
| Autor/in | Robert Simson |
| Verlag | Mathew Carey, and sold by J. Conrad & Company, S. F. Bradford, Birch & Small, and Samuel Etheridge. Printed by T. & G. Palmer, 116, High-Street., 1806 |
| Original von | University of Michigan |
| Digitalisiert | 11. Juni 2007 |
| Länge | 518 Seiten |
| Zitat exportieren | BiBTeX EndNote RefMan |