## 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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Page 120

If

If

**any two points be taken in the circumference of a circle , the right line which joins them**falls within the circle . For if possible let the right line joining them be such that it has a point outside the circle ; connect the centre ...### What people are saying - Write a review

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### Common terms and phrases

absurd adjacent altitude ANALYSIS arches assumed base centre chord circle circumference common construct describe diagonal diameter difference divided double draw drawn 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 Hence hypothenuse inscribed intercept internal intersect isosceles join less lesser line drawn lines be drawn magnitude mean meet Note 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

### Popular passages

Page 128 - The angle at the centre of a circle is double the angle at the circumference on the same arc.

Page 26 - 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.

Page 111 - In any triangle, the square of the side subtending an acute angle is less than the sum of the squares of the...

Page 4 - 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.

Page 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.

Page 2 - 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.

Page 20 - DE : but equal triangles on the same base and on the same side of it, are between the same parallels ; (i.

Page 116 - If any two points be taken in the circumference of a circle, the straight line which joins them shall fall within the circle.

Page 156 - 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.

Page 28 - Similar triangles are to one another in the duplicate ratio of their homologous sides.