## 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 65

ABD is = to

balf difference . From this it is evident , if from one extremity B , of the given base ,

you draw BA , making the angle DBA = to

...

ABD is = to

**half**the sum to**half**the difference , and . . ADB is = to**half**the sum —balf difference . From this it is evident , if from one extremity B , of the given base ,

you draw BA , making the angle DBA = to

**half**the suin +**half**the difference , and...

Side 71

ACB is

make at one extremity C of it , an angle BCA = to

vertical angle , produce the right line AC ' till CD is = to the given difference ; from

its ...

ACB is

**half**the supplement of the vertical angle . If . . . you draw any line , BC ,make at one extremity C of it , an angle BCA = to

**half**the supplement of thevertical angle , produce the right line AC ' till CD is = to the given difference ; from

its ...

Side 108

Describe on the line made up of the

common extremity of the given line and produced part draw a line par . to a side

of the 0 % , from the other extremity of the produced part dra v a diagonal and

through ...

Describe on the line made up of the

**half**and part pro . duced a 32 , from thecommon extremity of the given line and produced part draw a line par . to a side

of the 0 % , from the other extremity of the produced part dra v a diagonal and

through ...

Side 111

If a right line be cut into equal and also into unequal parts , the sum of the

squares of the unequal parts is equal to double the sum of the squares of the

and of the intermediate part . The Ol of the greater segment is = to a 0° of

of ...

If a right line be cut into equal and also into unequal parts , the sum of the

squares of the unequal parts is equal to double the sum of the squares of the

**half**and of the intermediate part . The Ol of the greater segment is = to a 0° of

**half**a 2of ...

Side 112

De of

produced line together with the 0 % of the produced part is = to double the 2 of

sum of ...

De of

**half**the given line , ( prop . 7 , b . 2 . ỹ Therefore the 0 % of the wholeproduced line together with the 0 % of the produced part is = to double the 2 of

**half**the given line and of the line made up of**half**and prodiced part . Cor . Thesum of ...

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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.