## 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 103

The rectangle under the sum and

between their squares . Because the rectangle together with the O2 of the less is

= to the o ' of the greater , as is evident from the preceding proposition , for the ...

The rectangle under the sum and

**difference**of two right lines is to the**differences**between their squares . Because the rectangle together with the O2 of the less is

= to the o ' of the greater , as is evident from the preceding proposition , for the ...

Side 104

For the

ers of the segments of the side upon which the perpendicular falls , ( cor . 4 , prop

. 47 , 1 , ) and . . when the perpendicular falls within the triangle to the rectangle ...

For the

**difference**between the grs of the sides is to the**difference**between tlieers of the segments of the side upon which the perpendicular falls , ( cor . 4 , prop

. 47 , 1 , ) and . . when the perpendicular falls within the triangle to the rectangle ...

Side 105

By being given the rectangle under any two lines and their

find the lines . For if the square of half the

the product will be = to the O2 of half the sum , ( for half the

By being given the rectangle under any two lines and their

**difference**, we canfind the lines . For if the square of half the

**difference**be added to the given rect .the product will be = to the O2 of half the sum , ( for half the

**difference**is = to the ... 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

the given quantity . Then it is evident from prop . 9 , b . 2 , that the O - rs of AD , DB

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 , DB

are ...

Side 181

Al is = to half the

then AS is = to JB ; for draw BH parallel to AC and join AH , which , on account of

the parrallels is = to BC , but BS by the proposition is = to half the

Al is = to half the

**difference**of AB , BC . . Cor . 2 . Let fall DS at right angles to AB ,then AS is = to JB ; for draw BH parallel to AC and join AH , which , on account of

the parrallels is = to BC , but BS by the proposition is = to half the

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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.