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

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Resultat 1-5 av 30

Side 109

Certain of the following properties have been proved in the Fifth Book ,

respecting four

which and where ; and prove the remaining ones . Hypothesis , A : B :: C : D ;

then ( 1 ) A : C ...

Certain of the following properties have been proved in the Fifth Book ,

respecting four

**proportional**magnitudes A , B , C , D : let the student point outwhich and where ; and prove the remaining ones . Hypothesis , A : B :: C : D ;

then ( 1 ) A : C ...

Side 112

If a straight line be drawn parallel to one of the sides of a triangle , it shall cut the

other sides , or these produced ,

produced , be cut

...

If a straight line be drawn parallel to one of the sides of a triangle , it shall cut the

other sides , or these produced ,

**proportionally**: and if the sides , or the sidesproduced , be cut

**proportionally**, the straight line which joins the points of section...

Side 113

Next , let the sides AB , AC of the triangle ABC , or these produced be cut

join DE : DE is parallel to BC . The same construction being made , because as

BD to ...

Next , let the sides AB , AC of the triangle ABC , or these produced be cut

**proportionally**in the points D , E , that is , so that BD be to DA , as CE to EA ; andjoin DE : DE is parallel to BC . The same construction being made , because as

BD to ...

Side 119

From this it is manifest , that the perpendicular drawn from the right angle of a

right - angled triangle to the base , is a mean

of the base , and also that each of the sides is a mean

From this it is manifest , that the perpendicular drawn from the right angle of a

right - angled triangle to the base , is a mean

**proportional**between the segmentsof the base , and also that each of the sides is a mean

**proportional**between the ... Side 120

To find a third

given straight lines , and let them be placed so as to contain any angle ; it is

required to find a third

E ; and ...

To find a third

**proportional**to two given straight lines . Let AB , AC be the twogiven straight lines , and let them be placed so as to contain any angle ; it is

required to find a third

**proportional**to AB , AC . Produce AB , AC , to the points D ,E ; and ...

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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.