## 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 131

PROB , From a given point without a given circle , to draw a right line which shall

be a

given point as distance , describe a circle , connect the centre and given point ...

PROB , From a given point without a given circle , to draw a right line which shall

be a

**tangent**to the circle . From the centre of the given circle as a centre and thegiven point as distance , describe a circle , connect the centre and given point ...

Side 139

Hence also can be drawn a

a right line from the given point to the centre of the circle , bisect it , and from the

point of bisection as centre , describe a circle to pass through the given point ...

Hence also can be drawn a

**tangent**to a circle from a given point without it : drawa right line from the given point to the centre of the circle , bisect it , and from the

point of bisection as centre , describe a circle to pass through the given point ...

Side 142

If from a point without a circle troo , right lines be drawn to it , one of which is a

and the external segment is equal to the square of the

...

If from a point without a circle troo , right lines be drawn to it , one of which is a

**tangent**to the circle and the other cuts it , the rectangle under the rohole secantand the external segment is equal to the square of the

**tangent**. 1 . Let the secant...

Side 158

HE , hecause OL is a

LE , and since OH is = to LE , HE is parallel to OL , : , the angle FHE is a right

angle . Then join the centres F , E ; and on FE describe a semicircle FHE , in it

inflect ...

HE , hecause OL is a

**tangent**the angles FOL , ÉLO are right , . . FH is parallel toLE , and since OH is = to LE , HE is parallel to OL , : , the angle FHE is a right

angle . Then join the centres F , E ; and on FE describe a semicircle FHE , in it

inflect ...

Side 61

... and position , such , that if from any point in the circumference straight lines be

drawn to the given points , and a

ratio .

... and position , such , that if from any point in the circumference straight lines be

drawn to the given points , and a

**tangent**to the given circle ; the o ? of the**tangent**shall have to the rectangle of the lines drawn to the given points a givenratio .

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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.