## The geometry, by T. S. Davies. Conic sections, by Stephen Fenwick |

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Resultat 1-5 av 91

Side 10

Wherefore , from the given point c , in the given straight line AB , FC has been

and because ABC is a stiaight line , the angle CBE is equal ( 10 Def . ) to the

angle ...

Wherefore , from the given point c , in the given straight line AB , FC has been

**drawn**at right angles to AB . ... From the point B**draw**BE at right angles to AB ;and because ABC is a stiaight line , the angle CBE is equal ( 10 Def . ) to the

angle ...

Side 20

To

A be the given point , and BC ... Therefore the straight line EAF is

the given point A parallel to the given straight line BC . Which was to be done .

To

**draw**a straight line through a given point parallel to a given straight line . LetA be the given point , and BC ... Therefore the straight line EAF is

**drawn**throughthe given point A parallel to the given straight line BC . Which was to be done .

Side 30

If through the vertex of an isosceles triangle a line be

it will bisect the angles at the vertex made by producing the equal sides of the

triangle . 3. The difference between any two sides of a triangle is less than the

third ...

If through the vertex of an isosceles triangle a line be

**drawn**parallel to the base ,it will bisect the angles at the vertex made by producing the equal sides of the

triangle . 3. The difference between any two sides of a triangle is less than the

third ...

Side 31

Prove also that if all the sides of a quadrilateral figure be bisected , and lines be

equal to half the given quadrilateral . 14. If the two diagonals of a parallelogram

be ...

Prove also that if all the sides of a quadrilateral figure be bisected , and lines be

**drawn**to join the adjacent points of bisection , they will form a parallelogramequal to half the given quadrilateral . 14. If the two diagonals of a parallelogram

be ...

Side 32

From the right angle of a triangle

an angle with one side equal to the ... Only one perpendicular can be

a given point to a given straight line , whether the point be in the line or without it .

From the right angle of a triangle

**draw**a line to meet the hypothenuse , makingan angle with one side equal to the ... Only one perpendicular can be

**drawn**froma given point to a given straight line , whether the point be in the line or without it .

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The geometry, by T. S. Davies. Conic sections, by Stephen Fenwick Royal Military Academy, Woolwich Uten tilgangsbegrensning - 1853 |

### Vanlige uttrykk og setninger

ABCD axis base bisected called centre circle circumference coincide common cone construction contained curve described diameter difference dihedral angles direction distance divided double draw drawn edges ellipse equal equal angles equimultiples extremities faces figure formed four fourth given line given point greater hence horizontal inclination intersection join less likewise magnitudes manner meet method multiple opposite parallel parallel planes parallelogram pass perpendicular perspective picture plane MN plane of projection plane PQ position preceding prism problem produced profile angles Prop proportional PROPOSITION proved ratio reason rectangle remaining respectively right angles SCHOLIUM segment shown sides similar sphere square straight line surface taken tangent Theor third touch trace transverse triangle triangle ABC trihedral vertex vertical Whence Wherefore whole

### Populære avsnitt

Side 19 - That, if a straight line falling on two straight lines make the interior angles on the same side less than two right angles, the two straight lines, if produced indefinitely, meet on that side on which are the angles less than the two right angles.

Side 35 - If a straight line be divided into two equal parts, and also into two unequal parts ; the rectangle contained by the unequal parts, together with the square on the line between the points of section, is equal to the square on half the line.

Side 4 - AB; but things which are equal to the same are equal to one another...

Side 128 - EQUIANGULAR parallelograms have to one another the ratio which is compounded of the ratios of their sides.* Let AC, CF be equiangular parallelograms, having the angle BCD equal to the angle ECG : the ratio of the parallelogram AC to the parallelogram CF, is the same with the ratio which is compounded of the ratios of their sides. Let BG, CG, be placed in a straight line ; therefore DC and CE are also in a straight line (14.

Side 8 - If two triangles have two sides of the one equal to two sides of the...

Side 36 - If a straight line be bisected and produced to any point, the rectangle contained by the whole line thus produced and the part of it produced...

Side 21 - BCD, and the other angles to the other angles, (4. 1.) each to each, to which the equal sides are opposite : therefore the angle ACB is equal to the angle CBD ; and because the straight line BC meets the two straight lines AC, BD, and makes the alternate angles ACB, CBD equal to one another, AC is parallel (27. 1 .) to DB ; and it was shown to be equal to it. Therefore straight lines, &c.

Side 65 - If a straight line touch a circle, and from the point of contact a straight line be drawn cutting the circle, the angles which this line makes with the line touching the circle shall be equal to the angles which are in the alternate segments of the circle.

Side 4 - Magnitudes which coincide with one another, that is, which exactly fill the same space, are equal to one another.

Side 116 - If two triangles have one angle of the one equal to one angle of the other and the sides about these equal angles proportional, the triangles are similar.