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 7
Page 177
A similar to the polygon FGHKL , the angle BAE is equal to the Book VI . angle
GFL a , and BA is to AE as GF to FL a : wherefore , be cause the triangles ABE ,
FGL have an angle in one equal to a 1.def.6 . an angle in the other , and their
sides ...
A similar to the polygon FGHKL , the angle BAE is equal to the Book VI . angle
GFL a , and BA is to AE as GF to FL a : wherefore , be cause the triangles ABE ,
FGL have an angle in one equal to a 1.def.6 . an angle in the other , and their
sides ...
Page 179
RECTILINEAL figures which are similar to the same rectilineal figure , are also
similar to one another . Let each of the rectilineal figures A , B be similar to the
rectilineal figure C : the figure A is similar to the figure B. Because A is similar to C
...
RECTILINEAL figures which are similar to the same rectilineal figure , are also
similar to one another . Let each of the rectilineal figures A , B be similar to the
rectilineal figure C : the figure A is similar to the figure B. Because A is similar to C
...
Page 182
Wherefore each of the parallelograms GE , KH is similar to DB : but rectilineal
figures which are similar to the same rectilineal figure , are also similar f 21. 6 . to
one anotherf ; therefore the parallelogram GE is similar to KH . Wherefore , the ...
Wherefore each of the parallelograms GE , KH is similar to DB : but rectilineal
figures which are similar to the same rectilineal figure , are also similar f 21. 6 . to
one anotherf ; therefore the parallelogram GE is similar to KH . Wherefore , the ...
Page 193
and they are upon equal straight lines BC , CK : but similar seg - Book VI . ments
of circles upon equal straight lines are equals to one another : therefore the
segment BXC is equal to the segment COK : g 24. 3 . and the triangle BGC is
equal to ...
and they are upon equal straight lines BC , CK : but similar seg - Book VI . ments
of circles upon equal straight lines are equals to one another : therefore the
segment BXC is equal to the segment COK : g 24. 3 . and the triangle BGC is
equal to ...
Page 258
AEH equal d and similar to the triangle HKD : for the same reason , the triangle
AGH is equal and similar to the triangle d 4. 1 . HLD : and because ihe two
straight lines EH , HG which meet one another are parallel to KD , DL that meet
one ...
AEH equal d and similar to the triangle HKD : for the same reason , the triangle
AGH is equal and similar to the triangle d 4. 1 . HLD : and because ihe two
straight lines EH , HG which meet one another are parallel to KD , DL that meet
one ...
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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 |