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 |
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Page 271
Therefore the rest of the cylinder , that B. XII . is , the prism of which the base is
the polygon AEBFCGDH , and of which the altitude is the same with that of the
cylinder , is greater than the triple of the cone : but this prism is triple d of d 1.
Therefore the rest of the cylinder , that B. XII . is , the prism of which the base is
the polygon AEBFCGDH , and of which the altitude is the same with that of the
cylinder , is greater than the triple of the cone : but this prism is triple d of d 1.
Page 272
Therefore the rest of the cone , that is , the pyramid , of which the base is the
polygon H AEBFCGDH , and of which the vertex is the same with that of the cone
, D is greater than the third part of the cylinder . But this pyramid is the third part of
...
Therefore the rest of the cone , that is , the pyramid , of which the base is the
polygon H AEBFCGDH , and of which the vertex is the same with that of the cone
, D is greater than the third part of the cylinder . But this pyramid is the third part of
...
Page 273
tex with the cone * , the pyramid inscribed in the cone is half B. XII . of the pyramid
circumscribed about it , because they are to one another as their bases a : but the
cone is less than the circum- a 6. 12 . scribed pyramid ; therefore the pyramid ...
tex with the cone * , the pyramid inscribed in the cone is half B. XII . of the pyramid
circumscribed about it , because they are to one another as their bases a : but the
cone is less than the circum- a 6. 12 . scribed pyramid ; therefore the pyramid ...
Page 275
EFGH as the cone AL to any solid which is less than the cone EN . In the same
manner it may be demonstrated that the circle EFGH is not to the circle ABCD as
the cone EN to any solid less than the cone AL . Nor can the circle ABCD be to
the ...
EFGH as the cone AL to any solid which is less than the cone EN . In the same
manner it may be demonstrated that the circle EFGH is not to the circle ABCD as
the cone EN to any solid less than the cone AL . Nor can the circle ABCD be to
the ...
Page 279
the cone ABCDL , so is the cone EFGHN to some solid , B. XII . which must be
less a than the cone ABCDL , because the solid Z is greater than the cone
EFGHN : therefore the cone EFGHN a 14. 5 . has to a solid which is less than the
cone ...
the cone ABCDL , so is the cone EFGHN to some solid , B. XII . which must be
less a than the cone ABCDL , because the solid Z is greater than the cone
EFGHN : therefore the cone EFGHN a 14. 5 . has to a solid which is less than the
cone ...
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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 |