## 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 119

Draw any right line within the circle , let it be terminated by the circumference ,

bisect it and from the point of bisection draw ... For if it be possible , let any other

point be the centre of the given circle , the right

of ...

Draw any right line within the circle , let it be terminated by the circumference ,

bisect it and from the point of bisection draw ... For if it be possible , let any other

point be the centre of the given circle , the right

**lines drawn**from it to the extremityof ...

Side 120

Then in the triangle of which the line connecting the assumed points is the base ,

the angles at the base are = , but one of the angles made by the

the centre to the point outside the circle , being external to one of those , is ...

Then in the triangle of which the line connecting the assumed points is the base ,

the angles at the base are = , but one of the angles made by the

**line drawn**fromthe centre to the point outside the circle , being external to one of those , is ...

Side 122

THEOR , If from any point within a circle , which is not the centre , righĩ

The remaining part of the diameter is the least . Those

THEOR , If from any point within a circle , which is not the centre , righĩ

**lines**be**drawn**to the circumference , the greatest is that which passes through the centre .The remaining part of the diameter is the least . Those

**lines**which make equal ... Side 10

Hence it is evident that if the altitude of an isosceles a be bisected , and right

whole A will be thus divided into four equal As . 2 . If the right

A ...

Hence it is evident that if the altitude of an isosceles a be bisected , and right

**lines**be**drawn**from the point of bisection to the extremities of the base , thewhole A will be thus divided into four equal As . 2 . If the right

**line**from any < of aA ...

Side 58

E and F draw right lines LEP , QFP intersecting in P . Required the locus of P ?

XVIII . If a right

divided in a given ratio , the locus of the point of section is a right line given in ...

E and F draw right lines LEP , QFP intersecting in P . Required the locus of P ?

XVIII . If a right

**line drawn**through a given point to a right line given in position bedivided in a given ratio , the locus of the point of section is a right line given in ...

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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.