## 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 8

connect its vertex with the given point ; the connecting line is at

given line . For thus there are formed two triangles having the three sides of one

respectively = to those of the other , . . . , & c . Schol . . In the same manner a ...

connect its vertex with the given point ; the connecting line is at

**right angles**to thegiven line . For thus there are formed two triangles having the three sides of one

respectively = to those of the other , . . . , & c . Schol . . In the same manner a ...

Side 15

If a right line intersect two right lines and makes the external angle equal to the

internal and opposite on the same side of the line , or makes the internal angles

on the same side together , equal to two

If a right line intersect two right lines and makes the external angle equal to the

internal and opposite on the same side of the line , or makes the internal angles

on the same side together , equal to two

**right angles**, the two right lines are ... Side 17

Hence in a triangle if one angle be right the : other two are together = to a

triangles have two angles = to two , the remaining angles are also equal . Cor . 3 .

Hence in a triangle if one angle be right the : other two are together = to a

**right****angle**; and if one angle be = to the other two , it is a**right angle**. . Cor . 2 . If twotriangles have two angles = to two , the remaining angles are also equal . Cor . 3 .

Side 18

If one angle of a parallelogram be a

For the adjacent angle is right , because with a

If one angle of a parallelogram be a

**right angle**, the other three are**right angles**.For the adjacent angle is right , because with a

**right angle**it is = to two**right****angles**, and the opposite are**right angles**, because they are = to these**right****angles**. Side 51

In the triangles DGC , GFI the sides DC and CG are respectively to GI and IF , and

the contained angles are = as being right , . . . the angle GFI is 10 DGC , . . the

angles DGC and FGI are to the angles FGI , GFL and . to a

a ...

In the triangles DGC , GFI the sides DC and CG are respectively to GI and IF , and

the contained angles are = as being right , . . . the angle GFI is 10 DGC , . . the

angles DGC and FGI are to the angles FGI , GFL and . to a

**right angle**, . . DGF isa ...

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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.