## 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 100

Page 8

... angles are at one point B , any one of ' them is expressed by three letters , of which the letter that is ' at the ...

... angles are at one point B , any one of ' them is expressed by three letters , of which the letter that is ' at the ...

**right angle**; and the straight line which stands on the other is called a perpendicular to it . XI . An obtuse angle is ... Page 12

...

...

**right angle**. XXVIII . An obtuse angled triangle is that which has an obtuse angle . XXIX . An acute angled triangle is that which has three acute angles ... angles**right angles**. XXXI . An oblong is that which has all its angles**right angles**... Page 14

...

...

**right angles**are equal to one another . XII . " If a straight line meets two straight lines , so as to make the " two interior angles on the same side of it taken together " less than two**right angles**, these straight lines being con ... Page 22

...

...

**right angles**to a given straight line , from a given point in the same . Let AB be a given straight line , and C a point given in it ; it is required to draw a straight line from the point C at right an- gles to AB . Take any point D in ... Page 23

... angle CHF is equal to the angle CHG ; and they are adjacent angles ; but when a straight line standing e 8. 1 . on a straight line makes the adjacent angles equal to one ano- ther , each of them is a

... angle CHF is equal to the angle CHG ; and they are adjacent angles ; but when a straight line standing e 8. 1 . on a straight line makes the adjacent angles equal to one ano- ther , each of them is a

**right angle**, and the straight line ...### Other editions - View all

### Common terms and phrases

altitude angle ABC angle BAC base BC BC is equal BC is given bisected Book XI centre circle ABCD circumference cone cylinder demonstrated described diameter draw drawn equal angles equiangular equimultiples Euclid excess fore given angle given in magnitude given in position given in species given magnitude given point given ratio given straight line gnomon greater join less Let ABC meet multiple opposite parallel parallelogram perpendicular point F polygon prisms proportionals proposition pyramid Q. E. D. PROP radius ratio of AE rectangle CB rectangle contained rectilineal figure right angles segment sides BA similar sine solid angle solid parallelepipeds square of AC straight line AB straight line BC tangent THEOR third triangle ABC triplicate ratio vertex wherefore

### 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.