## 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 96

Otherwise thus : A ssume a line = to either part . Then , the rectangle under this

assumed line and the whole line is = to the sum of the rectangles under the

assumed line and each of the parts , ( prop . 1 , b . 2 . ) but the

assumed ...

Otherwise thus : A ssume a line = to either part . Then , the rectangle under this

assumed line and the whole line is = to the sum of the rectangles under the

assumed line and each of the parts , ( prop . 1 , b . 2 . ) but the

**rect**. under theassumed ...

Side 100

Otherwise thus : Assume a line = to either part . Then , the rectangle under this

assumed line and the whole line is = to the sum of the rectangles under the

assumed line and each of the parts , ( prop . 1 , b . 2 . ) but the

assumed ...

Otherwise thus : Assume a line = to either part . Then , the rectangle under this

assumed line and the whole line is = to the sum of the rectangles under the

assumed line and each of the parts , ( prop . 1 , b . 2 . ) but the

**rect**. under theassumed ...

Side 109

Then the

balf the base and the O ' of the intercept between the point of bisection and other

point of section , ( prop . 5 and 6 , b . 2 , ) but the dif . between the o ' rs of half and

...

Then the

**rect**, under the former segments is to the difference between the ? ofbalf the base and the O ' of the intercept between the point of bisection and other

point of section , ( prop . 5 and 6 , b . 2 , ) but the dif . between the o ' rs of half and

...

Side 150

Angle AC , CD is to twice the area of ACD , . . the

area . . If therefore you produce the given difference until the

the area , it is evident that AC and CB are the sides of the required triangle , 23 .

Angle AC , CD is to twice the area of ACD , . . the

**rect**. ACB is to twice the givenarea . . If therefore you produce the given difference until the

**rect**. ACB is to twicethe area , it is evident that AC and CB are the sides of the required triangle , 23 .

Side 180

EAI with a

to the rectangle CE . For bisect AE is G join GO and let fall the perpendicular DF :

then GO is = to GE = { L , and the angle - FEO = AOF = TAL = ILA is to GOE ...

EAI with a

**rect**. DCI is = to the given reet . CE , . ' , & c . 2 . Also the O ' of OE - is =to the rectangle CE . For bisect AE is G join GO and let fall the perpendicular DF :

then GO is = to GE = { L , and the angle - FEO = AOF = TAL = ILA is to GOE ...

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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.