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 13
... produced ever so far both ways , do not meet . Book I. POSTULATES . I. LET it be granted that a straight line may be drawn from any one point to any other point . II . That a terminated straight line may be produced to any length in a ...
... produced ever so far both ways , do not meet . Book I. POSTULATES . I. LET it be granted that a straight line may be drawn from any one point to any other point . II . That a terminated straight line may be produced to any length in a ...
Seite 14
... produced , shall at length meet upon that side on " which are the angles which are less than two right angles . " See the notes on prop . 29. of book I. " PROPOSITION I. PROBLEM . TO describe an equilateral triangle upon 14 THE ELEMENTS.
... produced , shall at length meet upon that side on " which are the angles which are less than two right angles . " See the notes on prop . 29. of book I. " PROPOSITION I. PROBLEM . TO describe an equilateral triangle upon 14 THE ELEMENTS.
Seite 15
... produce the straight lines DA , DB to E and F ; from the centre B , at the distance BC , described the circle CGH , and from the centre D , at the distance DG , describe the circle GKL . AL shall be equal to BC . C K A iom . a 1. Post ...
... produce the straight lines DA , DB to E and F ; from the centre B , at the distance BC , described the circle CGH , and from the centre D , at the distance DG , describe the circle GKL . AL shall be equal to BC . C K A iom . a 1. Post ...
Seite 18
... produced to D and E ; the angle ABC shall be equal to the angle ACB , and the angle CBD to the angle BCE . a 3. 1 . b 4. 1 . In BD take any point F , and from AE the greater , cut off AG equala to AF , the less , and join FC , GB . F D ...
... produced to D and E ; the angle ABC shall be equal to the angle ACB , and the angle CBD to the angle BCE . a 3. 1 . b 4. 1 . In BD take any point F , and from AE the greater , cut off AG equala to AF , the less , and join FC , GB . F D ...
Seite 20
... produce AC , AD to E , F ; there- fore , because AC is equal to AD in the triangle ACD , the angles ECD , FDC upon the other side of the base CD are equal a to one another , but the angle ECD is greater than the angle BCD ; wherefore ...
... produce AC , AD to E , F ; there- fore , because AC is equal to AD in the triangle ACD , the angles ECD , FDC upon the other side of the base CD are equal a to one another , but the angle ECD is greater than the angle BCD ; wherefore ...
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The Elements of Euclid: The Errors, by Which Theon, Or Others, Have Long Ago ... Robert Simson,Robert Euclid Keine Leseprobe verfügbar - 2015 |
The Elements of Euclid: The Errors, by Which Theon, Or Others, Have Long Ago ... Robert Simson,Robert Euclid Keine Leseprobe verfügbar - 2022 |
The Elements of Euclid: The Errors, by Which Theon, Or Others, Have Long Ago ... Robert Simson,Robert Euclid Keine Leseprobe verfügbar - 2018 |
Häufige Begriffe und Wortgruppen
altitude angle ABC angle BAC base BC BC is equal BC is given bisected Book XI centre circle ABCD circumference cone cylinder demonstrated described diameter draw drawn equal angles equiangular equimultiples Euclid excess fore given angle given in magnitude given in position given in species given magnitude given point given ratio given straight line gnomon greater join less Let ABC meet multiple opposite parallel parallelogram perpendicular point F polygon prisms proportionals proposition pyramid Q. E. D. PROP radius ratio of AE rectangle CB rectangle contained rectilineal figure right angles segment sides BA similar sine solid angle solid parallelepipeds square of AC straight line AB straight line BC tangent THEOR third triangle ABC triplicate ratio vertex wherefore
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 |