## 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 107

ll , The square of the sum exceeds the difference of the squares by two

under the sum and lesser . 12 . ... The square of the greater of two lines exceeds

the

ll , The square of the sum exceeds the difference of the squares by two

**rectangles**under the sum and lesser . 12 . ... The square of the greater of two lines exceeds

the

**rectangle**under the greater and less , by a**rectangle**under greater and ... Side 113

The

is = to the square of the less segment , as is evident by taking the

the segments from the O ' of the greater segment and the

The

**rectangle**under the greater segment and difference between the segmentsis = to the square of the less segment , as is evident by taking the

**rectangle**underthe segments from the O ' of the greater segment and the

**rectangle**under given ... Side 114

The square of the whole line is also equal to two squares of the greater with a

the segments is = to a

square ...

The square of the whole line is also equal to two squares of the greater with a

**rectangle**under the segments . For one o of the greater with a**rectangle**underthe segments is = to a

**rectangle**under the whole and greater , . . & c . 5 . Thesquare ...

Side 193

The

under the perpendicular ( CD ) to the base and diameter ( CE ) of the circum.

scribing circle . Fig . 86 . . . villes Take CF = CB and CG = CD , join FG and AE ;

then ...

The

**rectangle**under the sides ( AC CB ) of any triangle is equal to the**rectangle**under the perpendicular ( CD ) to the base and diameter ( CE ) of the circum.

scribing circle . Fig . 86 . . . villes Take CF = CB and CG = CD , join FG and AE ;

then ...

Side 30

If three right lines be proportional , the

the square of the mean . And if the

square of the mean , the three right lines are proportional . Part 1 . Assume a right

...

If three right lines be proportional , the

**rectangle**under the extremes is equal tothe square of the mean . And if the

**rectangle**under the extremes be equal to thesquare of the mean , the three right lines are proportional . Part 1 . Assume a right

...

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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.