## The school edition. Euclid's Elements of geometry, the first six books, by R. Potts. corrected and enlarged. corrected and improved [including portions of book 11,12].1864 |

### From inside the book

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**one equal to two angles of the other , each to each , and**one side equal to one side , viz . either the sides adja- cent to the equal angles in each , or the sides opposite to them ; then shall the other sides be equal , each to each ... Page 178

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**one equal to two angles of the other , each to each ; and**the side BD , which is opposite to one of the equal angles in each , is common to both ; therefore their other sides are equal ; ( 1. 26. ) wherefore DE is equal to DF : for the ... Page 185

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**one equal to two angles of the other , each to each ; and**the side FC which is adjacent to the equal angles in each , is com- mon to both ; therefore the other sides are equal to the other sides , and the third angle to the third angle ... Page 187

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**one equal to two angles of the other , each to each ; and**the side FC , which is opposite to one of the equal angles in each , is common to both ; therefore the other sides are equal , each to each ; ( 1. 26. ) wherefore the ... Page 317

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**one equal to two angles of the other , each to each , and**the sides AE , EB , adjacent to the equal angles , equal to one another : wherefore they have their other sides equal : ( 1. 26. ) therefore GE is equal to EH , and AG to BH ...### Common terms and phrases

A₁ ABCD AC is equal Algebraically angle ABC angle ACB angle BAC angle equal Apply Euc base BC chord circle ABC constr describe a circle diagonals diameter divided double draw equal angles equiangular equilateral triangle equimultiples Euclid Euclid's Elements exterior angle Geometrical given angle given circle given line given point given straight line gnomon greater hypotenuse inscribed intersection isosceles triangle less Let ABC line BC lines be drawn multiple opposite angles parallelogram parallelopiped pentagon perpendicular polygon problem produced Prop proportionals proved Q.E.D. PROPOSITION radius ratio rectangle contained rectilineal figure remaining angle right angles right-angled triangle segment semicircle shew shewn similar solid angle square on AC tangent THEOREM touch the circle trapezium triangle ABC twice the rectangle vertex vertical angle wherefore

### Popular passages

Page 112 - Guido, with a burnt stick in his hand, demonstrating on the smooth paving-stones of the path, that the square on the hypotenuse of a right-angled triangle is equal to the sum of the squares on the other two sides.

Page 83 - If a straight line be bisected, and produced to any point ; the rectangle contained by the whole line thus produced, and the part of it produced, together with the square...

Page 48 - If two triangles have two sides of the one equal to two sides of the other, each to each ; and...

Page 238 - The first of four magnitudes is said to have the same ratio to the second, which the third has to the fourth, when any equimultiples whatsoever of the first and third being taken, and any equimultiples whatsoever of the second and fourth; if the multiple of the first be less than that of the second, the multiple of the third is also less than that of the fourth...

Page 198 - A LESS magnitude is said to be a part of a greater magnitude, when the less measures the greater, that is, ' when the less is contained a certain number of times exactly in the greater.

Page 271 - SIMILAR triangles are to one another in the duplicate ratio of their homologous sides.

Page 81 - If a straight line be divided into any two parts, the rectangle contained by the whole and one of the parts, is equal to the rectangle contained by the two parts, together with the square of the aforesaid part.

Page 115 - angle in a segment' is the angle contained by two straight lines drawn from any point in the circumference of the segment, to the extremities of the straight line which is the base of the segment.

Page 341 - On the same base, and on the same side of it, there cannot be two triangles...

Page 24 - ... twice as many right angles as the figure has sides ; therefore all the angles of the figure together with four right angles, are equal to twice as many right angles as the figure has sides.