## 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]. |

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Resultat 1-5 av 61

Side 44

It is of the highest importance to attain a clear conception of an angle , and of the

sum and

suggests the Geometrical conception of an angle , which may be regarded as

formed ...

It is of the highest importance to attain a clear conception of an angle , and of the

sum and

**difference**of two angles . The literal meaning of the term angulussuggests the Geometrical conception of an angle , which may be regarded as

formed ...

Side 47

If the line AB be equal to the A B C D line CD ; and if the line EF be also equal to

the line GH ; then the

following ...

If the line AB be equal to the A B C D line CD ; and if the line EF be also equal to

the line GH ; then the

**difference**of AB and EF , E _ F G _ 1 is equal to the**difference**of CD and GH . Axiom iv . admits of being exemplified under the twofollowing ...

Side 51

Prop . 111 . This problem admits of two solutions , and it is left undetermined from

which end of the greater line the part is to be cut off . By means of this problem , a

straight line may be found equal to the sum or the

Prop . 111 . This problem admits of two solutions , and it is left undetermined from

which end of the greater line the part is to be cut off . By means of this problem , a

straight line may be found equal to the sum or the

**difference**of two given lines . Side 54

It may be easily shewn from this proposition , that the

of a triangle is less than the third side . Prop . XXII . When the sum of two of the

lines is equal to , and when it is less than , the third line ; let the diagrams be ...

It may be easily shewn from this proposition , that the

**difference**of any two sidesof a triangle is less than the third side . Prop . XXII . When the sum of two of the

lines is equal to , and when it is less than , the third line ; let the diagrams be ...

Side 58

By this proposition may be found a square equal to the sum of any given squares

, or equal to any multiple of a given square : or equal to the

given squares . The truth of this proposition may be exhibited to the eye in some ...

By this proposition may be found a square equal to the sum of any given squares

, or equal to any multiple of a given square : or equal to the

**difference**of twogiven squares . The truth of this proposition may be exhibited to the eye in some ...

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### Vanlige uttrykk og setninger

ABCD Algebraically Apply base bisected Book chord circle circumference common construction contained definition demonstrated described diagonals diameter difference distance divided double draw drawn equal equal angles equiangular equilateral triangle equimultiples Euclid extremities fall figure formed four fourth Geometrical given circle given line given point given straight line greater half Hence inscribed intersection isosceles join length less Let ABC line drawn magnitudes manner mean meet multiple parallel parallelogram pass perpendicular plane problem produced Prop proportionals proved Q.E.D. PROPOSITION radius ratio reason rectangle rectangle contained regular remaining respectively right angles segment semicircle shew shewn sides similar solid square straight line taken tangent THEOREM third touch triangle ABC twice units vertex wherefore whole

### Populære avsnitt

Side 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.

Side 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...

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

Side 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...

Side 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.

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

Side 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.

Side 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.

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

Side 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.