## 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

Ergebnisse 1-5 von 80

Seite 7

and because the point B is the center of the circle ACE , therefore BC is equal to AB ; but it has been

and because the point B is the center of the circle ACE , therefore BC is equal to AB ; but it has been

**proved**that AC is equal to AB ; therefore AC , BC are each of them equal to AB ... Seite 10

and FC has been

and FC has been

**proved**to be equal to GB ; hence , because the two sides BF , FC are equal to the two CG , GB , each to each ; and the angle BFC has been**proved**to be ual to the angle CGB , also the base BC is common to the two ... Seite 16

But the angles CBE , EBD have been

But the angles CBE , EBD have been

**proved**equal to the same three angles ; and things which are equal to the same thing are equal to one another ; therefore the angles CBE , EBD are equal to the angles DBA , ABC ; but the angles CBE ... Seite 23

therefore the side EG is greater than the side EF ; but EG was

therefore the side EG is greater than the side EF ; but EG was

**proved**equal to BC ; therefore BC is greater than EF . Wherefore , if two triangles , & c . Q.E. D. PROPOSITION XXV . THEOREM . If two triangles have two sides of the one ... Seite 30

therefore the same angles of these triangles are equal to the angles of the figure together with four right angles ; but it has been

therefore the same angles of these triangles are equal to the angles of the figure together with four right angles ; but it has been

**proved**that the angles of the triangles are equal to twice as many right angles as the figure has sides ...### Was andere dazu sagen - Rezension schreiben

Es wurden keine Rezensionen gefunden.

### 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...