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 |
Im Buch
Ergebnisse 1-5 von 100
Seite 4
... magnitude . " Now this proposition is a theorem , not a definition ; because the equality of figures of any kind must be demonstrated , and not assumed ; and therefore , though this were a true proposition , it ought to have been ...
... magnitude . " Now this proposition is a theorem , not a definition ; because the equality of figures of any kind must be demonstrated , and not assumed ; and therefore , though this were a true proposition , it ought to have been ...
Seite 119
... magnitude is said to be a part of a greater magnitude , Book V. when the less measures the greater , that is , when the less is ' contained a certain number of times exactly in the greater . II . A greater magnitude is said to be a ...
... magnitude is said to be a part of a greater magnitude , Book V. when the less measures the greater , that is , when the less is ' contained a certain number of times exactly in the greater . II . A greater magnitude is said to be a ...
Seite 120
... Magnitudes which have the same ratio are called proportionals . N. B. When four magnitudes are proportionals , it is ... magnitude . For example , if A , B , C , D be four magnitudes of the same kind , the first A is said to have to the ...
... Magnitudes which have the same ratio are called proportionals . N. B. When four magnitudes are proportionals , it is ... magnitude . For example , if A , B , C , D be four magnitudes of the same kind , the first A is said to have to the ...
Seite 121
... magnitude ' of proportionals , so as that they continue still to be propor- ' tionals . ' XIII . Permutando , or alternando , by permutation , or alternately ; this word is used when there are four proportionals , and it is See N ...
... magnitude ' of proportionals , so as that they continue still to be propor- ' tionals . ' XIII . Permutando , or alternando , by permutation , or alternately ; this word is used when there are four proportionals , and it is See N ...
Seite 122
... magnitudes ' are taken two and two . ' XIX . Ex æquali , from equality ; this term is used simply by itself , when the first magnitude is to the second of the first rank , as the first to the second of the other rank ; and as the se ...
... magnitudes ' are taken two and two . ' XIX . Ex æquali , from equality ; this term is used simply by itself , when the first magnitude is to the second of the first rank , as the first to the second of the other rank ; and as the se ...
Andere Ausgaben - Alle anzeigen
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 |