## 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 13

Page 77

IF two circles touch each other internally , the straight line which

centres being produced shall pass through the ... if not , let it fall otherwise , if

possible , as FGDH , and

20.1 .

IF two circles touch each other internally , the straight line which

**joins**theircentres being produced shall pass through the ... if not , let it fall otherwise , if

possible , as FGDH , and

**join**AF , AG : and because AG , GF are greater a than a20.1 .

Page 217

DE ; EF , GH , HK , all equal to one another ; and

triangle may be made a of three straight lines equal a 22. 11 . АДА to AC , DF ,

GK . Let this be the triangle LMNb , so that AC 6 22. 1 . be equal to LM , DF to MN

, and ...

DE ; EF , GH , HK , all equal to one another ; and

**join**AC , DF , GK : then atriangle may be made a of three straight lines equal a 22. 11 . АДА to AC , DF ,

GK . Let this be the triangle LMNb , so that AC 6 22. 1 . be equal to LM , DF to MN

, and ...

Page 265

diameter , the triangle ABD is equal a to a 34. 1 . the triangle EBD ; therefore the

pyramid of which the base is the triangle ABD , and vertex the point C , is equal b

to ...

**Join**BD , EC , CD ; and because ABED is a parallelogram of which BD is thediameter , the triangle ABD is equal a to a 34. 1 . the triangle EBD ; therefore the

pyramid of which the base is the triangle ABD , and vertex the point C , is equal b

to ...

Page 273

... S , and

triangles EOF , FPG , GRH , HSE is greater than half of G А 00 回國 the segment

of the circle in which it is : upon each of these triangles erect a pyramid having

the same ...

... S , and

**join**EO , OF , FP , PG , GR , RH , HS , SE : therefore each of thetriangles EOF , FPG , GRH , HSE is greater than half of G А 00 回國 the segment

of the circle in which it is : upon each of these triangles erect a pyramid having

the same ...

Page 287

B D G A F U L M E circumferences BO , KS are equal , and OV , SQ are

perpendicular to their diameters , therefore d OV is equal to SQ ; d 26. 1 . and BV

equal to KQ ...

**Join**VQ ; and because in the equal semicircles BXD , KXN the R с P T H S 2B D G A F U L M E circumferences BO , KS are equal , and OV , SQ are

perpendicular to their diameters , therefore d OV is equal to SQ ; d 26. 1 . and BV

equal to KQ ...

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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.