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
Page 17
Wherefore the whole triangle ABC shall coincide with the whole triangle DEF , and be equal to it ; and the other angles of the one shall coincide with the remaining angles of the other , and be equal to them , viz . the angle ABC to the ...
Wherefore the whole triangle ABC shall coincide with the whole triangle DEF , and be equal to it ; and the other angles of the one shall coincide with the remaining angles of the other , and be equal to them , viz . the angle ABC to the ...
Page 18
1 . equal b to the base GB , and the triangle AFC to the triangle AGB ; and the remaining angles of the one are equal b to the remaining angles of the other , each to each , to which B В the equal sides are opposite ; viz . the angle ...
1 . equal b to the base GB , and the triangle AFC to the triangle AGB ; and the remaining angles of the one are equal b to the remaining angles of the other , each to each , to which B В the equal sides are opposite ; viz . the angle ...
Page 25
... ABD are likewise together equal to two right angles ; therefore the angles CBA , ABE are equal to the angles CBA , ABD : take away the common angle ABC , the remaining angle ABE is equal to the remaining angle b 3.
... ABD are likewise together equal to two right angles ; therefore the angles CBA , ABE are equal to the angles CBA , ABD : take away the common angle ABC , the remaining angle ABE is equal to the remaining angle b 3.
Page 26
1. AEB is equal b to the angle CEF , because they are opposite vertical angles ; therefore c 4. 1 . the base AB is equal < to the base CF , and the triangle AEB to the triangle CEF , and the remaining angles to the ...
1. AEB is equal b to the angle CEF , because they are opposite vertical angles ; therefore c 4. 1 . the base AB is equal < to the base CF , and the triangle AEB to the triangle CEF , and the remaining angles to the ...
Page 35
BGH ; therefore the remaining angle AGH is equal to the remaining angle GHD ; and they are alternate angles ; therefore AB is parallel to CD . Wherefore , if a straight line , & c . Q. E. D. PROP . XXIX .
BGH ; therefore the remaining angle AGH is equal to the remaining angle GHD ; and they are alternate angles ; therefore AB is parallel to CD . Wherefore , if a straight line , & c . Q. E. D. PROP . XXIX .
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The Elements of Euclid: The Errors, by Which Theon, Or Others, Have Long Ago ... Robert Simson,Robert Euclid No preview available - 2015 |
The Elements of Euclid: Viz. the First Six Books, Together with the Eleventh ... Robert Simson,Robert Euclid No preview available - 2016 |
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 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
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 |