## 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 - 518 sider |

### Fra bogen

Resultater 1-5 af 48

Side 319

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**given**a more explicit demonstration than that which is now in the Elements . PROP . X. B. V. It was necessary to give another demonstration of this pro-**position**, because that which is in the Greek and Latin , or other editions , is ... Side 324

... gave of conver- sion , is not legitimate , as Clavius has rightly observed , who has

... gave of conver- sion , is not legitimate , as Clavius has rightly observed , who has

**given**a good demonstration of it which we have put in pro-**position**E ; but he makes it a corollary from the 19th , and be- gins it with the words ... Side 341

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**position**of the sides which contain the figures , to one another , depending partly upon each of these : and , for ...**given**no definition of equal figures , and it is certain he did not give this : for what is Book XI . Book XI called ... Side 351

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**given**; but he does not demonstrate the second and third cases ; the ...**position**, because the planes containing the solids which are to be ...**mentioned**in this proposition are similar , that the equality of the solids in prop . 25 ... Side 367

... given , and the ratios of their sides given . IV . Points , lines , and spaces , are said to be

... given , and the ratios of their sides given . IV . Points , lines , and spaces , are said to be

**given in position**, which have always the same situation , and which are either actually exhibited , or can be found . A. An angle is said to be ...### Andre udgaver - Se alle

### Almindelige termer og sætninger

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

### Populære passager

Side 30 - Any two sides of a triangle are together greater than the third side.

Side 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.

Side 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...

Side 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.

Side 28 - If one side of a triangle be produced, the exterior angle is greater than either of the interior opposite angles.

Side 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.

Side 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.

Side 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.

Side 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.

Side 180 - Therefore, universally, similar rectilineal figures are to one another in the duplicate ratio of their homologous sides.