## 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 |

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Resultat 1-5 av 11

Side 51

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**gnomon**. ' rallelogram HG , together with the complements AF , ' FC , is the**gnomon**, which ' is more briefly expressed H by the letters AGK , or EHC , which are at the B ' opposite angles of the pa- D F K C G ' rallelograms which make ... Side 55

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**gnomon**CMG ; therefore the**gnomon**CMG is equal to the rectangle AD , DB : to each of these add LG , which is equal e to the square of CD ; therefore the**gnomon**CMG , together with LG , is equal to the rectangle AD , DB , together ... Side 56

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**gnomon**CMG and AM is the rect- angle contained by AD , DB , E G F e Cor . 4.2 . for DM is equal e to DB : therefore the**gnomon**CMG is equal to the rectangle AD , DB : add to each of these LG , which is equal to the square of CB ... Side 57

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**gnomon**AKF together with the square CK ; therefore the**gnomon**AKF , toge- ther with the square CK , is double of AK : but twice the rectangle AB , BC is double of AK , for BK is equal to BC : therefore the**gnomon**AKF , together with ... Side 58

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**gnomon**AOH are quadruple of AK : and because AK is the rectangle contained by AB , BC , for BK is equal to BC , four ...**gnomon**AOH . To each of these add XH , which is equal d to the square of AC : therefore four times the ...### Andre utgaver - Vis alle

The Elements of Euclid: Viz. the First Six Books, Together with the Eleventh ... Euclid Uten tilgangsbegrensning - 1810 |

### Vanlige uttrykk og setninger

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 avsnitt

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.