## 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 13

Those

one of the angles contained by the equal

anyle .

Those

**sides**will contain an angle = to the given an . gle . ... of the other , and ifone of the angles contained by the equal

**sides**be greater than the other , the**side**opposite the greater angle is greater than the**side**opposite to the leaseranyle .

Side 115

THEOR , In an obtuse angled triangle , the square of the

obtuse angle , exceeds the sum of the squares of the

obtuse angle , by double the rectangle under either of these

external ...

THEOR , In an obtuse angled triangle , the square of the

**side**subtending the "obtuse angle , exceeds the sum of the squares of the

**sides**which contain theobtuse angle , by double the rectangle under either of these

**sides**and theexternal ...

Side 116

perpendicular or the 2 of the

double the rectangle under the

intercept , is to the sum of the o ' rs of the other two

be right ...

perpendicular or the 2 of the

**side**opposite to the acute angle , . . . this withdouble the rectangle under the

**side**on which the perpendicular falls , andintercept , is to the sum of the o ' rs of the other two

**sides**. Schol . 1 . If the trianglebe right ...

Side 13

The bisecting line will always meet the

external or on the other

of an isosceles triangle is produced , the bisecting line will be then par . to the

base ...

The bisecting line will always meet the

**side**produced , either on the**side**of theexternal or on the other

**side**of it , except when the**side**about the vertical angleof an isosceles triangle is produced , the bisecting line will be then par . to the

base ...

Side 25

Equal parallelograms , which have one angle in each equal , have the

about the equal angles reciprocally ... By reciprocally proportional , is meant , that

a

...

Equal parallelograms , which have one angle in each equal , have the

**sides**about the equal angles reciprocally ... By reciprocally proportional , is meant , that

a

**side**about the = angle of the first : a**side**about the = angle of the second : : the...

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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.