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 - Trigonometry - 518 pages |
From inside the book
Results 1-5 of 9
Page 273
Vertex is put in place of altitude which is in the Greek , because the pyra . mid , in
what follows , is supposed to be circumscribed about the cone , and so must have
the same vertex . And the same change is made in some places fola lowing B.
Vertex is put in place of altitude which is in the Greek , because the pyra . mid , in
what follows , is supposed to be circumscribed about the cone , and so must have
the same vertex . And the same change is made in some places fola lowing B.
Page 361
demonstration , that the Greek editor did not perceive that Book XII . the
perpendicular drawn from the point K to the straight line BD must necessarily fall
upon the point V , for in the figure it is made to fall upon the point 2 a different
point from V ...
demonstration , that the Greek editor did not perceive that Book XII . the
perpendicular drawn from the point K to the straight line BD must necessarily fall
upon the point V , for in the figure it is made to fall upon the point 2 a different
point from V ...
Page 463
This is made more explicit than in the Greek text , to prevent a mistake which the
author of the second demonstration of the 24th proposition in the Greek edition
has fallen into , of think .. ing that a ratio is given to which another ratio is shown
to ...
This is made more explicit than in the Greek text , to prevent a mistake which the
author of the second demonstration of the 24th proposition in the Greek edition
has fallen into , of think .. ing that a ratio is given to which another ratio is shown
to ...
Page 465
V. The order of the propositions in the Greek text , betwech prop • 4 and prop . 25
, is now changed into another which is more natural , by placing those which are
more simple before those which are more complex ; and by placing together ...
V. The order of the propositions in the Greek text , betwech prop • 4 and prop . 25
, is now changed into another which is more natural , by placing those which are
more simple before those which are more complex ; and by placing together ...
Page 466
In the 23d prop . in the Greek text , which here is the 12th , the words , “ Mon 786
avras de , " are wrong translated by Claud . Hardy , in his edition of Euclid's Data ,
printed at Paris , anno 1625 , which was the first edition of the Greek text ; and ...
In the 23d prop . in the Greek text , which here is the 12th , the words , “ Mon 786
avras de , " are wrong translated by Claud . Hardy , in his edition of Euclid's Data ,
printed at Paris , anno 1625 , which was the first edition of the Greek text ; and ...
What people are saying - Write a review
We haven't found any reviews in the usual places.
Other editions - View all
The Elements of Euclid, Viz: The Errors, by Which Theon, Or Others, Have ... Robert Simson,Robert Euclid No preview available - 2018 |
The Elements of Euclid, Viz: The Errors, by Which Theon, Or Others, Have ... Robert Simson,Robert Euclid No preview available - 2015 |
The Elements of Euclid: Viz. The First Six Books, Together With the Eleventh ... Robert Simson No preview available - 2017 |
Common terms and phrases
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
Popular passages
Page 30 - Any two sides of a triangle are together greater than the third side.
Page 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.
Page 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...
Page 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.
Page 28 - If one side of a triangle be produced, the exterior angle is greater than either of the interior opposite angles.
Page 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.
Page 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.
Page 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.
Page 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.
Page 180 - Therefore, universally, similar rectilineal figures are to one another in the duplicate ratio of their homologous sides.
Bibliographic information
| Title | 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 |
| Author | Robert Simson |
| Publisher | 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 from | the University of Michigan |
| Digitized | 11 Jun 2007 |
| Length | 518 pages |
| Export Citation | BiBTeX EndNote RefMan |