## 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 57

Side 44

This has been restored from Proclus , as it seems to have a meaning in the

13 , Book vi . The definition of the segment of a circle is not once alluded to in

Book 1 ...

This has been restored from Proclus , as it seems to have a meaning in the

**construction**of Prop . 14 , Book ; the first case of Prop . 33 , Book ini , and Prop .13 , Book vi . The definition of the segment of a circle is not once alluded to in

Book 1 ...

Side 45

The postulates form The principles of

are , in fact , problems , the possibility of which is admitted to be self - evident ,

and to require no proof . It must , however , be carefully remarked , that the third ...

The postulates form The principles of

**construction**assumed in the Elements ; andare , in fact , problems , the possibility of which is admitted to be self - evident ,

and to require no proof . It must , however , be carefully remarked , that the third ...

Side 48

A proposition , as the term imports , is something proposed ; it is a problem ,

when some Geometrical

theorem when some Geo . metrical property is to be demonstrated . Every

proposition is ...

A proposition , as the term imports , is something proposed ; it is a problem ,

when some Geometrical

**construction**is required to be effected : and it is atheorem when some Geo . metrical property is to be demonstrated . Every

proposition is ...

Side 50

The determination contains the predicate in particular terms , as it is pointed out

in the diagram , and directs attention to the demonstration , by pronouncing the

thing sought . 4 . The

EUCLID ...

The determination contains the predicate in particular terms , as it is pointed out

in the diagram , and directs attention to the demonstration , by pronouncing the

thing sought . 4 . The

**construction**applies the postulates to prepare the 50EUCLID ...

Side 51

The

demonstration . 5 . The demonstration is the connexion of syllogisms , which

prove the truth or falsehood of the theorem , the possibility or impossibility of the

problem , in ...

The

**construction**applies the postulates to prepare the diagram for thedemonstration . 5 . The demonstration is the connexion of syllogisms , which

prove the truth or falsehood of the theorem , the possibility or impossibility of the

problem , in ...

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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.