## The Elements of geometry [Euclid book 1-3] in general terms, with notes &c. &c. Also a variety of problems & theorems. [Ed. by J. Luby. With] The elements of plane geometry, comprising the definitions of the fifth book, and the sixth book in general terms, with notes [&c.] by J. Luby [described as] Pt. 3 |

### Inni boken

Resultat 1-5 av 5

Side 17

... one of the * * legs from the vertex and constructing on it an equilateral : triangle

, and bisecting the angle of it cut off from the given right angle . I Cor . 6 . All the

internal angles of any rectilineal fie gure together with

... one of the * * legs from the vertex and constructing on it an equilateral : triangle

, and bisecting the angle of it cut off from the given right angle . I Cor . 6 . All the

internal angles of any rectilineal fie gure together with

**four**right angles are = to ... Side 67

The square of the hypothenuse ( AC ) of an isosceles right angled triangle ( AEC

) is equal to

on the hypothenuse . Fig . 19 . For ED is = to AD or DC : but the squares of AE ...

The square of the hypothenuse ( AC ) of an isosceles right angled triangle ( AEC

) is equal to

**four**times the square of the perpendicular ( ED ) from the right angleon the hypothenuse . Fig . 19 . For ED is = to AD or DC : but the squares of AE ...

Side 110

8 , THEOR , If a right line be divided into any two parts , the square of the sum of

the whole line and either seg . ment , is equal to

the whole line and that segment together with the square of the other segment .

8 , THEOR , If a right line be divided into any two parts , the square of the sum of

the whole line and either seg . ment , is equal to

**four**times the rectangle underthe whole line and that segment together with the square of the other segment .

Side 159

AB2 is of CD ' , but AB ' is to

must be = to ED2 which is of CD ' , . ; . EF is = to 4 ED . PROP . 8 . PROB . Given

of any triangle , the base , vertical angle and difference of the sides , to find it .

AB2 is of CD ' , but AB ' is to

**four**times AE * =**four**times EF ? , . . .**four**times EF ?must be = to ED2 which is of CD ' , . ; . EF is = to 4 ED . PROP . 8 . PROB . Given

of any triangle , the base , vertical angle and difference of the sides , to find it .

Side 6

By permutando or alternando ; when it is concluded , that if there be

magnitudes of the same kind proportionals , the first is to the third as the second

to the fourth . Note . In this the antecedents are compared with one another , and

the ...

By permutando or alternando ; when it is concluded , that if there be

**four**magnitudes of the same kind proportionals , the first is to the third as the second

to the fourth . Note . In this the antecedents are compared with one another , and

the ...

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The Elements of geometry [Euclid book 1-3] in general terms, with notes &c ... Euclides Uten tilgangsbegrensning - 1833 |

### Vanlige uttrykk og setninger

absurd adjacent ANALYSIS arches assumed base centre chord circle circumference common construct describe diagonal diameter difference divided double draw draw a line equal evident external extremity figure formed four fourth given angle given circle given in position given line given point given right line greater half hypothenuse inscribed intercept internal intersect isosceles join less lesser line drawn lines be drawn magnitude mean meet Note O’rs opposite side parallel parallelogram pass perpendicular point of bisection point of contact PROB produced PROP proportional proposition proved radii radius reason rect rectangle remaining required triangle respectively right angled triangle right angles right line segment semicircle side similar square stand subtending Suppose taken tangent THEOR third touch triangle unequal vertex whole line

### Populære avsnitt

Side 130 - The angle at the centre of a circle is double the angle at the circumference on the same arc.

Side 28 - IF three straight lines be proportionals, the rectangle contained by the extremes is equal to the square of the mean ; and if the rectangle contained by the extremes be equal to the square of the mean, the three straight lines are proportionals.

Side 113 - In any triangle, the square of the side subtending an acute angle is less than the sum of the squares of the...

Side 6 - A straight line is said to be cut in extreme and mean ratio, when the whole is to the greater segment as the greater segment is to the less.

Side 98 - If a straight line be divided into any two parts, the square of the whole line is equal to the squares of the two parts, together with twice the rectangle contained by the parts.

Side 4 - Convertendo ; when it is .concluded, that if there be four magnitudes proportional, the first is to the sum or difference of the first and second, as the third is to the sum or difference of the third and fourth.

Side 20 - DE : but equal triangles on the same base and on the same side of it, are between the same parallels ; (i.

Side 118 - If any two points be taken in the circumference of a circle, the straight line which joins them shall fall within the circle.

Side 158 - The sum of the squares of the sides of any quadrilateral is equal to the sum of the squares of the diagonals plus four times the square of the line joining the middle points of the diagonals.

Side 30 - Similar triangles are to one another in the duplicate ratio of their homologous sides.