## 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 100

Euclides James Luby. This rectangle is = to the square of one part with the

rectangle under the parts . For it is the rectangle under the

part on which the o ' is described ; if then the o ' be taken away , the remainder

will be the ...

Euclides James Luby. This rectangle is = to the square of one part with the

rectangle under the parts . For it is the rectangle under the

**whole line**and thatpart on which the o ' is described ; if then the o ' be taken away , the remainder

will be the ...

Side 109

Then the ' of given line is = to a rect . under the

complemental rect . and a 0 % of the other segment ; add to both be D ' of the

other segment : then the o ' rs of given line and one seg . are together = : to a rect

...

Then the ' of given line is = to a rect . under the

**whole line**and one segment , acomplemental rect . and a 0 % of the other segment ; add to both be D ' of the

other segment : then the o ' rs of given line and one seg . are together = : to a rect

...

Side 110

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

the

the

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 113

Euclides James Luby. pendicular , ( prop . 47 , 1 , ) take away the 2 of the half

, then the rect . under the

off the given

Euclides James Luby. pendicular , ( prop . 47 , 1 , ) take away the 2 of the half

**line**, then the rect . under the

**whole**produced**line**and produced part is = to the o ?off the given

**line**, if . . the rectangle under the perpendicular and produced part ... Side 114

The square of the

rectangle under the segments . For one o of the greater with a rectangle under

the segments is = to a rectangle under the whole and greater , . . & c . 5 . The

square ...

The square of the

**whole line**is also equal to two squares of the greater with arectangle under the segments . For one o of the greater with a rectangle under

the segments is = to a rectangle under the whole and greater , . . & c . 5 . The

square ...

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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.