## 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 |

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Resultat 1-5 av 5

Side 102

part and

intermediate and

the unequal segments , if . , the square of intermediate part be added to both , two

...

part and

**lesser**seg . together with the DJ ? of**lesser**seg , . two rectangles underintermediate and

**lesser**seg . with the 2 of**lesser**are together = to a rect . underthe unequal segments , if . , the square of intermediate part be added to both , two

...

Side 106

The sum of the squares of any two lines exceeds the difference of the squares by

two squares of the

sum and dif . or to a 12 of the dif . and two rect . under ,

The sum of the squares of any two lines exceeds the difference of the squares by

two squares of the

**lesser**. , . ; . ' For the difference of the ' rs is = to a rect . under .sum and dif . or to a 12 of the dif . and two rect . under ,

**lesser**and difference ... Side 114

The square of the line compounded of half the greater segment and the

segment is = to five times the square of half the greater segment . It is evident that

the ' of half the greater segment is the fourth part of the rect . under the whole line

...

The square of the line compounded of half the greater segment and the

**lesser**segment is = to five times the square of half the greater segment . It is evident that

the ' of half the greater segment is the fourth part of the rect . under the whole line

...

Side 32

and the greater base : the assumed part in the duplicate ratio of the greater to

ratio of those bases , which bases are homologous sides . Note . We can then cut

...

and the greater base : the assumed part in the duplicate ratio of the greater to

**lesser**base ( Def . 10 . 6 . ) . . . the given As are to one another in the duplicateratio of those bases , which bases are homologous sides . Note . We can then cut

...

Side 37

B . 6 ) . . . the rectangle under the whole line and

O ' of the greater , for the greater segment is a mean proportional between the

given line and

B . 6 ) . . . the rectangle under the whole line and

**lesser**segment shall be = to theO ' of the greater , for the greater segment is a mean proportional between the

given line and

**lesser**; if . . . you cut the given line , as in Prop . XI . Book 2 . the ...### Hva folk mener - Skriv en omtale

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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.