## 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]. |

### Inni boken

Resultat 6-10 av 81

Side 50

Every proposition , when complete , may be

pointed out in his commentary . 1 . The proposition , or general enunciation ,

which states in general terms the conditions of the problem or theorem . 2 .

Every proposition , when complete , may be

**divided**into six parts , as Proclus haspointed out in his commentary . 1 . The proposition , or general enunciation ,

which states in general terms the conditions of the problem or theorem . 2 .

Side 53

9 , it bisects the angle which is the defect of the angle BAC from frur right angles .

By means of this problem , any angle may be

c . equal angles . Prop . x . A finite straight line may , by this problem , be

...

9 , it bisects the angle which is the defect of the angle BAC from frur right angles .

By means of this problem , any angle may be

**divided**into four , eight , sixteen , &c . equal angles . Prop . x . A finite straight line may , by this problem , be

**divided**...

Side 57

If the given rectilineal figure have more than four sides , it may be

triangles by drawing straight lines from any angle of the figure to the opposite

angles , and then a parallelogram equal to the third triangle can be applied to LM

, and ...

If the given rectilineal figure have more than four sides , it may be

**divided**intotriangles by drawing straight lines from any angle of the figure to the opposite

angles , and then a parallelogram equal to the third triangle can be applied to LM

, and ...

Side 58

it will be obvious , that the squares will be

squares , each of the same magnitude ; and that the number of the small squares

into which the squares on the perpendicular and base are

...

it will be obvious , that the squares will be

**divided**into 9 , 16 and 25 smallsquares , each of the same magnitude ; and that the number of the small squares

into which the squares on the perpendicular and base are

**divided**is equal to the...

Side 59

This Book may be

properties of triangles , both with respect to their sides and angles ; and the

comparison of these mutually , both with regard to equality and inequality . The

second ...

This Book may be

**divided**into three parts . The first part treats of the origin andproperties of triangles , both with respect to their sides and angles ; and the

comparison of these mutually , both with regard to equality and inequality . The

second ...

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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.