## 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 1

certain number of times exactly ; for example , 3 is an aliquot part of 15 ; for it

measures , or is contained in it exactly 5 times ; but 4 is not a submultiple of 15 ,

for it is ...

**Note**. One magnitude is said to measure another when it is contained in it acertain number of times exactly ; for example , 3 is an aliquot part of 15 ; for it

measures , or is contained in it exactly 5 times ; but 4 is not a submultiple of 15 ,

for it is ...

Side 6

consequents with one another ; thus if A ; B : : C : D , by permutando A : C : : B : D

. If 1 : 2 : : 3 : 6 , permutando 1 : 3 : : 2 : 6 . This definition differs from those

following ; in it it ...

**Note**. In this the antecedents are compared with one another , and theconsequents with one another ; thus if A ; B : : C : D , by permutando A : C : : B : D

. If 1 : 2 : : 3 : 6 , permutando 1 : 3 : : 2 : 6 . This definition differs from those

following ; in it it ...

Side 28

is founded ; in it we are given three terms of an analogy to find a fourth ; if the

given terms be the extremes , and a mean , we can find the other mean , for the ...

**Note**1 . It is on principles similar to those of this proposition , that ther ule of threeis founded ; in it we are given three terms of an analogy to find a fourth ; if the

given terms be the extremes , and a mean , we can find the other mean , for the ...

Side 29

one of the acute s , it will meet the opposite side produced . The extremity of the

diameter being connected with the extremity of the subtending side adjacent to ...

**Note**3 . In Cor . 3 , if the given Abe obtuse , and the perpendicular be let fall fromone of the acute s , it will meet the opposite side produced . The extremity of the

diameter being connected with the extremity of the subtending side adjacent to ...

Side 37

the series will be found by taking each consequent from its antecedent ; for in any

analogy the first term is to the second as the difference between the first and ...

**Note**2 . It will also be seen , by the doctrine of ratios , that the successive terms ofthe series will be found by taking each consequent from its antecedent ; for in any

analogy the first term is to the second as the difference between the first and ...

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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.