## 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 13

PROPOSITION IX . PROBLEM . To bisect a given rectilineal angle , that is , to

required to bisect it . DHE в с In AB take any point D ; from AC cut off AE equal to

AD , ( 1 .

PROPOSITION IX . PROBLEM . To bisect a given rectilineal angle , that is , to

**divide**it into two equal angles . Let BAC be the given rectilineal angle . It isrequired to bisect it . DHE в с In AB take any point D ; from AC cut off AE equal to

AD , ( 1 .

Side 29

EKN в For any rectilineal figure ABCDE can be

the figure has sides , by drawing straight lines from a point F within the figure to

each of its angles . Then , because the three interior angles of a triangle are

equal ...

EKN в For any rectilineal figure ABCDE can be

**divided**into as many triangles asthe figure has sides , by drawing straight lines from a point F within the figure to

each of its angles . Then , because the three interior angles of a triangle are

equal ...

Side 42

The definitions in Euclid ' s Elements may be

which merely explain the meaning of the terms employed , and those , which ,

besides explaining the meaning of the terms , suppose the existence of the things

...

The definitions in Euclid ' s Elements may be

**divided**into two classes , thosewhich merely explain the meaning of the terms employed , and those , which ,

besides explaining the meaning of the terms , suppose the existence of the things

...

Side 44

... as in certain conic lines . ” Def . xx ! V - XXIX . Triangles are

classes , by reference to the relations of their sides ; and into three other classes ,

by reference to their angles . A further classification may be made by considering

...

... as in certain conic lines . ” Def . xx ! V - XXIX . Triangles are

**divided**into threeclasses , by reference to the relations of their sides ; and into three other classes ,

by reference to their angles . A further classification may be made by considering

...

Side 48

The propositions in Euclid ' s Elements of Geometry may be

classes , problems and theorems . A proposition , as the term imports , is

something proposed ; it is a problem , when some Geometrical construction is

required to be ...

The propositions in Euclid ' s Elements of Geometry may be

**divided**into twoclasses , problems and theorems . A proposition , as the term imports , is

something proposed ; it is a problem , when some Geometrical construction is

required to be ...

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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.