## 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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Side

Dr . Whewell , in his “ Thoughts on the Study of Mathematics , " has maintained ,

that mathematical studies judiciously pursued , form one of the most effective

means of developing and cultivating the

...

Dr . Whewell , in his “ Thoughts on the Study of Mathematics , " has maintained ,

that mathematical studies judiciously pursued , form one of the most effective

means of developing and cultivating the

**reason**: and that “ the object of a liberul...

Side 21

therefore the exterior angle BDC of the triangle CDE is greater than the interior

and opposite angle CED ; for the same

triangle ABE is greater than the interior and opposite angle BAC ; lie . Rae and it

has ...

therefore the exterior angle BDC of the triangle CDE is greater than the interior

and opposite angle CED ; for the same

**reason**, the exterior angle CED of thetriangle ABE is greater than the interior and opposite angle BAC ; lie . Rae and it

has ...

Side 32

wa But if the sides AD , EF , opposite to the base BC , be not terminated in the

same point ; Then , because ABCD is a parallelogram , therefore AD is equal to

BC ; ( 1 . 34 . ) and for a similar

to ...

wa But if the sides AD , EF , opposite to the base BC , be not terminated in the

same point ; Then , because ABCD is a parallelogram , therefore AD is equal to

BC ; ( 1 . 34 . ) and for a similar

**reason**, EF is equal to BC ; wherefore AD is equalto ...

Side 33

... therefore the parallelogram ABCD is equal to the parallelogram EBCH . ( I . 35 .

) For the same

EBCH ; . therefore the parallelogram ABCD is equal to the parallelogram EFGH .

... therefore the parallelogram ABCD is equal to the parallelogram EBCH . ( I . 35 .

) For the same

**reason**, the parallelogram EFGH is equal to the parallelogramEBCH ; . therefore the parallelogram ABCD is equal to the parallelogram EFGH .

Side 37

and for the same

Wherefore the two triangles AEK , KGC are equal to the two triangles AHK , KFC ,

( ax . 2 . ) but the whole triangle ABC is equal to the whole triangle ADC ;

therefore the ...

and for the same

**reason**, the triangle KGC is equal to the triangle KFC .Wherefore the two triangles AEK , KGC are equal to the two triangles AHK , KFC ,

( ax . 2 . ) but the whole triangle ABC is equal to the whole triangle ADC ;

therefore the ...

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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.