## 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 |

### Inni boken

Resultat 1-5 av 5

Side 109

2 , ) but the dif . between the

Ders of the first drawn line and a side of triangle , . . & c . But if the line drawn to

the base be perpendicular to it , it bisects the base , and the rectangle under the ...

2 , ) but the dif . between the

**o ' rs**of half and intercept is to the dif . between theDers of the first drawn line and a side of triangle , . . & c . But if the line drawn to

the base be perpendicular to it , it bisects the base , and the rectangle under the ...

Side 116

perpendicular or the 2 of the side opposite to the acute angle , . . . this with

double the rectangle under the side on which the perpendicular falls , and

intercept , is to the sum of the

be right ...

perpendicular or the 2 of the side opposite to the acute angle , . . . this with

double the rectangle under the side on which the perpendicular falls , and

intercept , is to the sum of the

**o ' rs**of the other two sides . Schol . 1 . If the trianglebe right ...

Side 146

other right line AG ( = to it ] to meet the produced part ; then , because AC and AG

are , the rectangle under CB , BG is = to the dif . between the

( cor . prop . 1 , b . 2 , ) but the rect . CBD is also = to it , which is absurd , .

other right line AG ( = to it ] to meet the produced part ; then , because AC and AG

are , the rectangle under CB , BG is = to the dif . between the

**O ' rs**of AB and AC ,( cor . prop . 1 , b . 2 , ) but the rect . CBD is also = to it , which is absurd , .

Side 147

Therefore bisect the given line in C , and cut its half CB so that the Oʻ of the

intermediate part shall be : = to half the difference between two

the given quantity . Then it is evident from prop . 9 , b . 2 , that the

are ...

Therefore bisect the given line in C , and cut its half CB so that the Oʻ of the

intermediate part shall be : = to half the difference between two

**o ' rs**of half andthe given quantity . Then it is evident from prop . 9 , b . 2 , that the

**O - rs**of AD , DBare ...

Side 148

The hypothenuse being given , the sum of the D ' rs is " given , . . . the difference

between the sum of the

rectangles under the sides , add this to the sum of the ' Oirs and their product is ...

The hypothenuse being given , the sum of the D ' rs is " given , . . . the difference

between the sum of the

**o ' rs**and 0 % of the difference is given ; which is to tworectangles under the sides , add this to the sum of the ' Oirs and their product is ...

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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.