## 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

Side 3

A circle is a plane figure contained by one line , which is called the circumference

, and is such that all straight

the circumference , are equal to one another . XVI . And this point is called the ...

A circle is a plane figure contained by one line , which is called the circumference

, and is such that all straight

**lines drawn**from a certain point within the figure tothe circumference , are equal to one another . XVI . And this point is called the ...

Side 14

To

in the same . Let AB be the given straight

required to

AC ...

To

**draw**a straight**line**at right angles to a given straight**line**, from a given pointin the same . Let AB be the given straight

**line**, and C a given point in it . It isrequired to

**draw**a straight**line**from the point C at right angles to AB . B D C E InAC ...

Side 15

It is required to

the other side of AB take any point D , and from ... Then the straight

.

It is required to

**draw**a straight**line**perpendicular to AB from the point C . B Uponthe other side of AB take any point D , and from ... Then the straight

**line**CH**drawn**from the given point C , shall be perpendicular to the given straight**line**AB.

Side 35

In the same manner it can be demonstrated , that no other

AD is parallel to BC ; AD is therefore parallel to BC . Wherefore , equal triangles

upon , & c . Q . E . D . PROPOSITION XL . THEOREM . Equal triangles upon

equal ...

In the same manner it can be demonstrated , that no other

**line drawn**from A butAD is parallel to BC ; AD is therefore parallel to BC . Wherefore , equal triangles

upon , & c . Q . E . D . PROPOSITION XL . THEOREM . Equal triangles upon

equal ...

Side 43

Def . 11 . Every visible

conception of the length only of the

Def . 11 . Every visible

**line**has both length and breadth , and it is impossible to**draw**any**line**whatever which shall have no breadth . The definition requires theconception of the length only of the

**line**to be considered , abstracted from , and ...### Hva folk mener - Skriv en omtale

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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.