## 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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Side 136

From the preceding

intercept equal arches are parallel , because the alterua te angles are equal ,

and vice versa . whole , the angle it is angle stands also = , . PROP . 28 , THEOR .

From the preceding

**proposition**, it is evident that in a circle , right lines whichintercept equal arches are parallel , because the alterua te angles are equal ,

and vice versa . whole , the angle it is angle stands also = , . PROP . 28 , THEOR .

Side 9

same altitude , are to one another as their bases . Part 1 . Let the antecedent -

base be divided into any number of = parts , and let one of those parts be

repeated as ...

**PROPOSITION**I . THEOREM . Triangles and parallelograms which have thesame altitude , are to one another as their bases . Part 1 . Let the antecedent -

base be divided into any number of = parts , and let one of those parts be

repeated as ...

Side 12

Note 1 . If the right line bisecting the external angle of a triangle , when produced

meet the base , it will divide it into segments proportional to the other two sides .

The demonstration of this is precisely the same as that of the

...

Note 1 . If the right line bisecting the external angle of a triangle , when produced

meet the base , it will divide it into segments proportional to the other two sides .

The demonstration of this is precisely the same as that of the

**proposition**, except...

Side 18

The demonstration is the same as that of the foregoing

assistance of this

which shall be to one another in a given ratio , by dividing the base of the given A

...

The demonstration is the same as that of the foregoing

**proposition**. Note . By theassistance of this

**proposition**, we may divide a given A into any number of Äswhich shall be to one another in a given ratio , by dividing the base of the given A

...

Side 26

From this

parallelograms whose bases and altitudes are reciprocally proportional , are

equal . Cor . 2 . If two triangles have two sides reciprocally proportional to two ,

and the ...

From this

**proposition**, and the preceding , it is evident , that triangles andparallelograms whose bases and altitudes are reciprocally proportional , are

equal . Cor . 2 . If two triangles have two sides reciprocally proportional to two ,

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.