## 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 125

If the given lines be at the same side of that passing through the centre , join the

centre and their extremities at the

formed , having a joining line and common side in one respectively to the other ...

If the given lines be at the same side of that passing through the centre , join the

centre and their extremities at the

**circumference**, then there are two trianglesformed , having a joining line and common side in one respectively to the other ...

Side 132

Let one side of the angle at the

because in the triangle formed by two radii and the line not passing through the

centre , those radii ares , the angles contained by eacb of them and the line pot ...

Let one side of the angle at the

**circumference**pass through the centre ; thenbecause in the triangle formed by two radii and the line not passing through the

centre , those radii ares , the angles contained by eacb of them and the line pot ...

Side 133

terminous with the cut side , and that at the centre contained by the produced part

and uncut side , is double of that at the

connecting line and cutting side ; if those latter angles be taken away the

remainder of ...

terminous with the cut side , and that at the centre contained by the produced part

and uncut side , is double of that at the

**circumference**contained by theconnecting line and cutting side ; if those latter angles be taken away the

remainder of ...

Side 40

proved to be as the arcs on which they stand ; it follows that the < s at the

necessary to prove , that the sectors of the same or equal circles standing on

equal arcs are = ...

proved to be as the arcs on which they stand ; it follows that the < s at the

**circumference**are so . In the proof of that part concerning the sectors , it isnecessary to prove , that the sectors of the same or equal circles standing on

equal arcs are = ...

Side 58

... the other will also terminate in a given

drawn through a given point to the

given ratio ; the locus of the point of section will also be the

given ...

... the other will also terminate in a given

**circumference**. XXI . If a right line ,drawn through a given point to the

**circumference**of a given o be divided in agiven ratio ; the locus of the point of section will also be the

**circumference**of agiven ...

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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.