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
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Page 262
B. XII . in the pyramid ABCG to the two prisms in the pyramid DEFH : and so are
the two prisms in the pyramid OMNG to ... may be shown of the prisms made by
dividing the pyramids AKLO and DPRS , and of all made by the same number of
...
B. XII . in the pyramid ABCG to the two prisms in the pyramid DEFH : and so are
the two prisms in the pyramid OMNG to ... may be shown of the prisms made by
dividing the pyramids AKLO and DPRS , and of all made by the same number of
...
Page 263
the base DEF , as the pyramid ABCG to any solid which is less B. XII . than the
pyramid DEFH . In the same manner it may be demonstrated , that the base DEF
is not to the base ABC as the pyramid DEFH to any solid which is less than the ...
the base DEF , as the pyramid ABCG to any solid which is less B. XII . than the
pyramid DEFH . In the same manner it may be demonstrated , that the base DEF
is not to the base ABC as the pyramid DEFH to any solid which is less than the ...
Page 264
See N. PYRAMIDS of the same altitude which have polygons for their bases , are
to one another as their bases . ... N , be of the same altitude : as the base ABCDE
to the base FGHKL , so is the pyramid ABCDEM to the pyramid FGHKLN .
See N. PYRAMIDS of the same altitude which have polygons for their bases , are
to one another as their bases . ... N , be of the same altitude : as the base ABCDE
to the base FGHKL , so is the pyramid ABCDEM to the pyramid FGHKLN .
Page 265
therefore , ex æquali c , as the base ABCDE to the base FGHKL , B. XII . so the
pyramid ABCDEM to the pyramid FGHKLN . Therefore , pyramids , & c . Q. E. D. c
22. 5 . PROP . VII . THEOR . EVERY prism having a triangular base may be ...
therefore , ex æquali c , as the base ABCDE to the base FGHKL , B. XII . so the
pyramid ABCDEM to the pyramid FGHKLN . Therefore , pyramids , & c . Q. E. D. c
22. 5 . PROP . VII . THEOR . EVERY prism having a triangular base may be ...
Page 269
altitude of the pyramid ABCG : therefore , as the base ABC to B. XII . the base
DEF , so is the altitude of the pyramid DEFH to the altitude of the pyramid ABCG :
wherefore the bases and altitudes of the pyramids ABCG , DEFH are reciprocally
...
altitude of the pyramid ABCG : therefore , as the base ABC to B. XII . the base
DEF , so is the altitude of the pyramid DEFH to the altitude of the pyramid ABCG :
wherefore the bases and altitudes of the pyramids ABCG , DEFH are reciprocally
...
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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 |