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 sider |
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Resultat 1-5 av 7
Side 300
13 , book 1. This part must therefore have been added to prop . 5 , upon account
of some proposition betwixt the 5th and 13th , but none of these stand in need of
it except the 7th proposition , on account of which it has been added : besides ...
13 , book 1. This part must therefore have been added to prop . 5 , upon account
of some proposition betwixt the 5th and 13th , but none of these stand in need of
it except the 7th proposition , on account of which it has been added : besides ...
Side 340
In the Greek , as also in the Latin translation , the words á stums , “ any whatever ,
” are left out in the demonstration of both parts of the proposition , and are now
added as quite necessary ; and in the demonstration of the second part , where ...
In the Greek , as also in the Latin translation , the words á stums , “ any whatever ,
” are left out in the demonstration of both parts of the proposition , and are now
added as quite necessary ; and in the demonstration of the second part , where ...
Side 369
The limitation within the inverted commas is not in the Greek text , but is now
necessarily added ; and the same must be understood in all the propositions of
the book which depend upon this second proposition , where it is not expressly ...
The limitation within the inverted commas is not in the Greek text , but is now
necessarily added ; and the same must be understood in all the propositions of
the book which depend upon this second proposition , where it is not expressly ...
Side 465
... magnitudes E , Z , C , a fourth proportional A may be found ; but this cannot
always be done by the Elements of Euclid ; from which it is plain Euclid must
have understood the proposition under the limitation which is now added to his
text .
... magnitudes E , Z , C , a fourth proportional A may be found ; but this cannot
always be done by the Elements of Euclid ; from which it is plain Euclid must
have understood the proposition under the limitation which is now added to his
text .
Side 468
Each of these has a determination , which is now added , which occasions a
change in their demonstrations . PROP . XXXVII , XXXIX , XL , XLI . The 35th and
36th propositions in the Greek text are joined into one , which makes the 39th in
this ...
Each of these has a determination , which is now added , which occasions a
change in their demonstrations . PROP . XXXVII , XXXIX , XL , XLI . The 35th and
36th propositions in the Greek text are joined into one , which makes the 39th in
this ...
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Vanlige uttrykk og setninger
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 Q. E. D. PROP radius reason rectangle rectangle contained 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 30 - Any two sides of a triangle are together greater than the third side.
Side 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.
Side 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...
Side 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.
Side 28 - If one side of a triangle be produced, the exterior angle is greater than either of the interior opposite angles.
Side 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.
Side 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.
Side 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.
Side 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.
Side 180 - Therefore, universally, similar rectilineal figures are to one another in the duplicate ratio of their homologous sides.
Bibliografisk informasjon
| Tittel | 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 |
| Forfatter | Robert Simson |
| Utgiver | 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 fra | University of Michigan |
| Digitalisert | 11. jun 2007 |
| Lengde | 518 sider |
| Eksporter sitat | BiBTeX EndNote RefMan |