## Euclid's Elements of Geometry: Chiefly from the Text of Dr. Simson, with Explanatory Notes; a Series of Questions on Each Book; and a Selection of Geometrical Exercises from the Senate-house and College Examination Papers, with Hints, &c. Designed for the Use of the Junior Classes in Public and Private Schools. the first six books, and the portions of the eleventh and twelfth books read at Cambridge |

### Im Buch

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Seite 6

**Magnitudes**which coincide with one another , that is , which exactly fill the same space , are equal to one another . IX . The whole is greater than its part . X. Two straight lines cannot enclose a space . XI . Seite 42

It is by experience we become acquainted with the existence of indi . vidual forms of

It is by experience we become acquainted with the existence of indi . vidual forms of

**magnitudes**; but by the mental process of abstraction , which begins with a particular instance , and proceeds to the general idea of alĩ objects of ... Seite 46

It is by experience we first become acquainted with the different forms of geometrical

It is by experience we first become acquainted with the different forms of geometrical

**magnitudes**, and the axioms , or the fundamental ideas of their equality or inequality appear to rest on the same basis . The conception of the truth ... Seite 47

Two geometrical

Two geometrical

**magnitudes**are equal , when they coincide or may be made to coincide : two abstract numbers are equal ... and two concrete numbers are equal , when they contain the same number of units of the same kind of**magnitude**. Seite 48

It may be observed that when equal

It may be observed that when equal

**magnitudes**are taken from unequal**magnitudes**, the greater remainder exceeds the less remainder by as much as the greater of the unequal**magnitudes**exceeds the less . If unequals be taken from unequals ...### Was andere dazu sagen - Rezension schreiben

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### Häufige Begriffe und Wortgruppen

ABCD Algebraically angle BAC 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 join less Let ABC line drawn magnitudes manner mean meet multiple opposite sides parallel parallelogram pass perpendicular plane problem produced Prop proportionals PROPOSITION proved Q.E.D. PROPOSITION radius ratio reason rectangle rectangle contained regular remaining respectively right angles segment semicircle shew shewn sides similar solid square taken tangent THEOREM third touch triangle ABC twice units vertex wherefore whole

### Beliebte Passagen

Seite 6 - If a straight line meets two straight lines, so as to make the two interior angles on the same side of it taken together less than two right angles...

Seite 118 - 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.

Seite 2 - When a straight line standing on another straight line makes the adjacent angles equal to one another, each of the angles is called a right angle ; and the straight line which stands on the other is called a perpendicular to it.

Seite 317 - If two triangles have two angles of the one equal to two angles of the other, each to each, and one side equal to one side, viz.

Seite 90 - If a straight line be divided into any two parts, the squares of the whole line, and of one of the parts, are equal to twice the rectangle contained by the whole and that part, together with the square of the other part. Let the straight line AB be divided into any two parts in the point C; the squares of AB, BC are equal to twice the rectangle AB, BC, together with the square of AC.

Seite 88 - If a straight line be divided into two equal parts, and also into two unequal parts; the rectangle contained by the unequal parts, together with the square of the line between the points of section, is equal to the square of half the line.

Seite 30 - ... 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.

Seite 9 - THE angles at the base of an isosceles triangle are equal to one another : and, if the equal sides be produced, the angles upon the other side of the base shall be equal.

Seite 22 - IF two triangles have two sides of the one equal to two sides of the other, each to each, but the angle contained by the two sides of one of them greater than the angle contained by the two sides equal to them, of the other ; the base of that which has the greater angle shall be greater than the base of the other...

Seite 92 - If a straight line be divided into two equal, and also into two unequal parts, the squares on the two unequal parts are together double of the square on half the line and of the square on the line between the points of section. Let the straight line AB be divided into two equal parts...