## 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 158

Then

right liné FH = to the sum of the radii FO , LE ,

and

tangent ...

Then

**join**the centres F , E ; and on FE describe a semicircle FHE , in it inflect aright liné FH = to the sum of the radii FO , LE ,

**join**HE , draw EL parallel to HFand

**join**LO : LO is the tangent ; the demonstration is evident . Also a directtangent ...

Side 165

Bisect DB and EI in K , H

are = ( by hypoth . ) and the angles AKC , AHC = ( by prop . b . 3 Elr . ) and AC

common AK is = to AH , ( prop , 26 . b . 1 . Elr . ) . . DB is = to IE ( prop . b . 3 Elr ) .

Bisect DB and EI in K , H

**join**A K and AH , Then , because the angles ACH , ACKare = ( by hypoth . ) and the angles AKC , AHC = ( by prop . b . 3 Elr . ) and AC

common AK is = to AH , ( prop , 26 . b . 1 . Elr . ) . . DB is = to IE ( prop . b . 3 Elr ) .

Side 176

Then

produce it to meet the circumference in E and I , EI is the line required to be

drawn . For ,

the ...

Then

**join**AP , upon it describe a semicircle POA inflect in it PO = to half F andproduce it to meet the circumference in E and I , EI is the line required to be

drawn . For ,

**join**OA : then because POA is right EI is bisected in 0 . . OP is halfthe ...

Side 180

For bisect AE is G

{ L , and the angle - FEO = AOF = TAL = ILA is to GOE ; also the angle CLA = LAE

is = to FOF . . . the angle CLI is = to FOG and LCI to OFG and OG to IL .

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 ; also the angle CLA = LAE

is = to FOF . . . the angle CLI is = to FOG and LCI to OFG and OG to IL .

Side 181

For draw PX at right angles to BC produced and

Elr . ) BI is to BX and PI to PX ; also AP is = to PC . . AI is = to CX ond . . IB , BX are

together to AB , BC together , but IB is = to balf the former quantity , and . . to half ...

For draw PX at right angles to BC produced and

**join**BP ; then ( prop . 26 . b . l .Elr . ) BI is to BX and PI to PX ; also AP is = to PC . . AI is = to CX ond . . IB , BX are

together to AB , BC together , but IB is = to balf the former quantity , and . . to half ...

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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.