## 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 10

Pre of them perils at the side mal angle is proved greater than the other internal

remote angle by producing the opposite side beyond the vertex of this

angle , and proving as before the new

Pre of them perils at the side mal angle is proved greater than the other internal

remote angle by producing the opposite side beyond the vertex of this

**external**angle , and proving as before the new

**external**angle , thus formed greater than ... Side 16

Let a right line be drawn outting the three given lines , this drawn line makes with

each pair of parallel lines an

same side of the line , and . . does so with the pair to be . proved parallel PROP .

Let a right line be drawn outting the three given lines , this drawn line makes with

each pair of parallel lines an

**external**angle = to an internal or remote on thesame side of the line , and . . does so with the pair to be . proved parallel PROP .

Side 17

The

each

. ) Therefore , all the

The

**external**angles of anr rectilineal figure are together to four right angles . Foreach

**external**angle , with the adjacent internal , is to iwo right angles , ( prop . 13. ) Therefore , all the

**external**angles , with all the internal , are 3 to ' lwice as ... Side 127

Then in the triangle formed by those connecting lines , the lines connecting the

centres and that of the internal circle with a point of contact , are together greater

than the line connecting the centre of the

Then in the triangle formed by those connecting lines , the lines connecting the

centres and that of the internal circle with a point of contact , are together greater

than the line connecting the centre of the

**external**circle with this point of contact ... Side 142

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 secant

and 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 secant

and the

**external**segment is equal to the square of the tangent . 1 . Let the secant...

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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.