## Elements of Geometry: Containing the First Six Books of Euclid, with a Supplement of the Quadrature of the Circle and the Geometry of Solids |

### From inside the book

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Page 7

... All right angles are equal to one another . " Two straight lines , which intersect one another , cannot be " both parallel to the same straight line . " Book I. Book I. late .

... All right angles are equal to one another . " Two straight lines , which intersect one another , cannot be " both parallel to the same straight line . " Book I. Book I. late .

**PROPOSITION**I. PROBLEM . TO describe OF GEOMETRY . 7. Page 8

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**PROPOSITION**I. PROBLEM . TO describe an equilateral triangle upon a given finite straight line . Let AB be the given straight line ; it is required to des- cribe an equilateral triangle upon it . From the centre A , at the distance AB ... Page 33

... divided into as many triangles as the figure has E D C sides , by drawing straight lines frora a point F within the figure A B to each of its angles . And , by the preceding

... divided into as many triangles as the figure has E D C sides , by drawing straight lines frora a point F within the figure A B to each of its angles . And , by the preceding

**proposition**, E a 2 Cor . 15. 1 . Book I. all OF GEOMETRY . 3.3 / Page 47

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**proposition**is placed here , because it is more connected with the first book than with any other . It is use- ful for explaining the nature of Hadley's sextant , and , though involved in the explanations usually given of that ... Page 50

... BG = A ; and BK = BG.BD = A.BD ; and DL = DK.DE = A.DE , becaused DK = BG = A . In like manner , EH = A.EC . Therefore KLH A A.BC = A.BD + A.DE + A.EC ; that is. d 34. 1 . * See the figure of the last

... BG = A ; and BK = BG.BD = A.BD ; and DL = DK.DE = A.DE , becaused DK = BG = A . In like manner , EH = A.EC . Therefore KLH A A.BC = A.BD + A.DE + A.EC ; that is. d 34. 1 . * See the figure of the last

**proposition**. 50 ELEMENTS.### Other editions - View all

### Common terms and phrases

ABC is equal altitude angle ABC angle ACB angle BAC angle contained angle EDF arch base BC bisected Book centre circle ABC circumference coincide common section cylinder definition demonstrated diameter draw drawa equal angles equiangular equilateral polygon equimultiples Euclid exterior angle fore four right angles given circle given straight line greater inscribed interior and opposite join less Let ABC Let the straight meet multiple opposite angle parallelogram parallelogram ABCD perpendicular point F polygon prism PROB produced proportional proposition pyramid Q. E. D. COR Q. E. D. PROP ratio rectangle contained rectilineal figure remaining angle segment solid angle solid parallelepipeds straight line AB straight line AC Suppl THEOR third touches the circle triangle ABC triangle DEF

### Popular passages

Page 121 - If two triangles have two angles of the one equal to two angles of the other, each to each, and one side equal to one side, viz. either the sides adjacent to the equal...

Page 42 - TO a given straight line to apply a parallelogram, which shall be equal to a given triangle, and have one of its angles equal to a given rectilineal angle.

Page 63 - Therefore, in obtuse-angled triangles, &c. QED PROP. XIII. THEOREM. In every triangle, the square of the side subtending either of the acute angles is less than the squares of the sides containing that angle, by twice the rectangle contained by either of these sides, and the straight line intercepted between the perpendicular let fall upon it from the opposite angle, and the acute angle.

Page 3 - A circle is a plane figure contained by one line, which is called the circumference, and is such that all straight lines drawn from a certain point within the figure to the circumference, are equal to one another.

Page 183 - Equiangular parallelograms have to one another the ratio which is compounded of the ratios of their sides. Let AC, CF be equiangular parallelograms having the angle BCD equal to the angle ECG ; the ratio of the parallelogram AC to the parallelogram CF is the same with the ratio which is compounded •f the ratios of their sides.

Page 3 - A diameter of a circle is a straight line drawn through the centre, and terminated both ways by the circumference.

Page 291 - 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 sides.

Page 160 - ... extremities of the base shall have the same ratio which the other sides of the triangle have to one...

Page 10 - ... shall be greater than the base of the other. Let ABC, DEF be two triangles, which have the two sides AB, AC, equal to the two DE, DF, each to each, viz.

Page 14 - Therefore, upon the same base, and on the same side of it, there cannot be two triangles that have their sides which are terminated in one extremity of the base equal to one another, and likewise those which are terminated in the other extretnity equal to one another.