## 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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Side 18

Right lines which join the

also themselves equal and parallel , Draw a diagonal , then two triangles are

formed , have ing a given = side , and diagonal in one respectively = to the other

...

Right lines which join the

**adjacent**extremities of equat and parallel right lines arealso themselves equal and parallel , Draw a diagonal , then two triangles are

formed , have ing a given = side , and diagonal in one respectively = to the other

...

Side 24

It can be proved that each of those parallelograms is respectively to the D ? on

that side of the triangle which is

that side and the hypothenuse be added to the angles of their o ' rs which are ...

It can be proved that each of those parallelograms is respectively to the D ? on

that side of the triangle which is

**adjacent**to it . For if the acute angle contained bythat side and the hypothenuse be added to the angles of their o ' rs which are ...

Side 13

but in this case it must be drawn from that extremity

the bisecting line meets the produced part . Note 2 . The bisecting line will always

meet the side produced , either on the side of the external or on the other side ...

but in this case it must be drawn from that extremity

**adjacent**to the point in whichthe bisecting line meets the produced part . Note 2 . The bisecting line will always

meet the side produced , either on the side of the external or on the other side ...

Side 38

From the right draw a perpendicular to the hypochenuse ; then the hypothenuse :

one of the sides about the right < : : that side : the

hypothenuse ( Cor . 8 . 6 ) , . . the figure upon the hypothenuse : to the similar

figure ...

From the right draw a perpendicular to the hypochenuse ; then the hypothenuse :

one of the sides about the right < : : that side : the

**adjacent**segment of thehypothenuse ( Cor . 8 . 6 ) , . . the figure upon the hypothenuse : to the similar

figure ...

Side 49

If from the vertical < of a A two lines be drawn to the base , making = ss with the

contained by the

Athere be ...

If from the vertical < of a A two lines be drawn to the base , making = ss with the

**adjacent**sides , the ' s of those sides will be proportional to the rectanglescontained by the

**adjacent**segments of the base . XLIX . If from the vertex of aAthere be ...

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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.