## 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 1-5 av 71

Side 13

To

BAC be the given rectilineal angle . It is required to

any point ... Wherefore the angle BAC is

...

To

**bisect**a given rectilineal angle , that is , to divide it into two equal angles . LetBAC be the given rectilineal angle . It is required to

**bisect**it . DHE в с In AB takeany point ... Wherefore the angle BAC is

**bisected**by the straight line AF . Q . E . F...

Side 18

... the angle ACD is greater than the angle BĂE or BAC . In the same manner , if

the side BC be

the angle BCG , that is , the angle ACD , ( 1 . 15 . ) is greater than the angle ABC .

... the angle ACD is greater than the angle BĂE or BAC . In the same manner , if

the side BC be

**bisected**, and AC be produced to G ; it may be demonstrated thatthe angle BCG , that is , the angle ACD , ( 1 . 15 . ) is greater than the angle ABC .

Side 61

Shew how a given straight line may be

do the lines which

or more than one of the corresponding opposite sides of the triangles ? 44 .

Shew how a given straight line may be

**bisected**by Euc . 1 . 1 . 43 . In what casesdo the lines which

**bisect**the interior angles of plane triangles , also**bisect**one ,or more than one of the corresponding opposite sides of the triangles ? 44 .

Side 63

lelogram , when its diagonals

into four triangles , which are equal , two ... same parts , shew that the straight line

joining the vertices of the triangles is

lelogram , when its diagonals

**bisect**each other : and when its diagonals divide itinto four triangles , which are equal , two ... same parts , shew that the straight line

joining the vertices of the triangles is

**bisected**by the line containing the bases . Side 65

be joined by a straight line AB , and this line be

perpendicular be drawn from the point of

described with any point in the perpendicular as a center ANCIENT

GEOMETRICAL ...

be joined by a straight line AB , and this line be

**bisected**in D , then if aperpendicular be drawn from the point of

**bisection**, it is manifest that a circledescribed with any point in the perpendicular as a center ANCIENT

GEOMETRICAL ...

### Hva folk mener - Skriv en omtale

Vi har ikke funnet noen omtaler på noen av de vanlige stedene.

### 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.