## 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. 31821 |

### From inside the book

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Page 127

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**point of contact**. For if possible let the centres be so situated , that the right line connecting them will not pass through a**point of contact**; produce it both ways to meet the circum- ferences , and connect the**point of contact**with ... Page 128

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**point of contact**. Then the right lines drawn from the centre of the lesser circle to the**points of contact**are , ( def . 15 , b . 1 , ) add to both the right line joining the centres , then the right line joining the centres and a ... Page 130

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**point of contact**, it cuts the circle . PART 1. For if it be possible , let there be a right line which meets it again and is perpendicular to the dia- imeter , connect the centre and this**point of contact**. Then because in the triangle ... Page 131

... point as distance , describe a circle , connect the centre and given point ... contact is per- pendicular to it , For if possible let any other right line ...

... point as distance , describe a circle , connect the centre and given point ... contact is per- pendicular to it , For if possible let any other right line ...

**point of contact**subtends a right angle , it is greater than the other line ... Page 132

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**point of contact**, passes through the centre of the circle . For if possible let the centre be without this line , join it and the**point of contact**; this joining line is at right angles to the tangent , ( prop . 18 , b . 3 , ) .. the ...### Other editions - View all

### Common terms and phrases

adjacent ANALYSIS angle ABC angle contained arches bisecting line chord circumference connecting line conterminous dedu describe a circle diagonal diameter directum divided draw a right drawn line equiangular equilateral triangle evident external angle extremity given angle given circle given in position given line given point given ratio given right line given side gonal half the given hypothenuse inscribed intercept intersect isosceles triangle less lesser let fall line bisecting lines be drawn magnitude mean proportional meet middle point opposite angle opposite side parallelogram pass pendicular perpen perpendicular point of bisection point of contact point of section polygons PORISMS PROB PROP radii radius rect rectangle required triangle right angled triangle right line drawn segts semicircle semiperimeter side subtending square Suppose tangent THEOR triangle ABC vertex vertical angle 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.