## 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 71

Side

...

chronic complaints and established maladies , no cure can be effected by

physicians of the body : of this , no cure can be effected by physicians of the mind

: for with ...

...

**hence**its designation of compound ignorance . In like manner , as of manychronic complaints and established maladies , no cure can be effected by

physicians of the body : of this , no cure can be effected by physicians of the mind

: for with ...

Side 10

and FC has been proved to be equal to GB ;

FC are equal to the two CG , GB , each to each ; and the angle BFC has been

proved to be equal to the angle CGB , also the base BC is common to the two ...

and FC has been proved to be equal to GB ;

**hence**, because the two sides BF ,FC are equal to the two CG , GB , each to each ; and the angle BFC has been

proved to be equal to the angle CGB , also the base BC is common to the two ...

Side 11

... the less equal to the greater , which is absurd . ( ax . 9 . ) Therefore AB is not

unequal to A C , that is , AB is equal to AC . Wherefore , if two angles , & c . Q . E .

D . COR .

... the less equal to the greater , which is absurd . ( ax . 9 . ) Therefore AB is not

unequal to A C , that is , AB is equal to AC . Wherefore , if two angles , & c . Q . E .

D . COR .

**Hence**an equiangular triangle is also equilateral . PROPOSITION VII . Side 24

... wherefore also the angle GCB is equal to the angle ACB ; ( ax . 1 . ) , the less

angle equal to the greater , which is impossible ; therefore AB is not unequal to

DE , that is , AB is equal to DE .

...

... wherefore also the angle GCB is equal to the angle ACB ; ( ax . 1 . ) , the less

angle equal to the greater , which is impossible ; therefore AB is not unequal to

DE , that is , AB is equal to DE .

**Hence**, in the triangles ABC , DEF ; because AB...

Side 25

hyp . ) and the included angle ABC is equal to the includedangle DEF ; ( hyp . ) )

therefore the base AC is equal to the base DF , ( 1 . 4 . ) and the third angle BAC

...

**Hence**, in the triangles ABC , DEF ; because AB is equal to DE , and BC to EF , (hyp . ) and the included angle ABC is equal to the includedangle DEF ; ( hyp . ) )

therefore the base AC is equal to the base DF , ( 1 . 4 . ) and the third angle BAC

...

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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.