## Elements of Geometry and Conic Sections |

### Inni boken

Resultat 1-5 av 22

Side 10

D Angles , like other quantities , may be added , subtracted ,

divided . Thus , the angle BCD is the sum of the two angles BCE , ECD ; and the

angle ECD is the difference between the two angles BCD , BCĚ . 10. When a

straight ...

D Angles , like other quantities , may be added , subtracted ,

**multiplied**, ordivided . Thus , the angle BCD is the sum of the two angles BCE , ECD ; and the

angle ECD is the difference between the two angles BCD , BCĚ . 10. When a

straight ...

Side 38

For , since the four quantities are proportional , А С BD

equal quantities by B ( Axiom 1 ) . we obtain Вхс A D

last equals by D , we have AxD = BXC . Cor . If there are three proportional ...

For , since the four quantities are proportional , А С BD

**Multiplying**each of theseequal quantities by B ( Axiom 1 ) . we obtain Вхс A D

**Multiplying**each of theselast equals by D , we have AxD = BXC . Cor . If there are three proportional ...

Side 42

I. , AXD = BxC ; or ,

A'xD ' = B'XC ; and

= B * XC % . Therefore , by Prop . II . , A ' : B ' :: C : D ' , and Al : B :: C :: D ' .

I. , AXD = BxC ; or ,

**multiplying**each of these equals by itself ( Axiom 1 ) , we haveA'xD ' = B'XC ; and

**multiplying**these last equals by AxD = B * C , we have A® XD '= B * XC % . Therefore , by Prop . II . , A ' : B ' :: C : D ' , and Al : B :: C :: D ' .

Side 62

Now , since KF is equal to AG , the area of the trapezoid is equal to DEXKF .

Hence the area of a trapezoid is equal to its altitude ,

joins the middle points of the sides which are not parallel . PROPOSITION VIII .

Now , since KF is equal to AG , the area of the trapezoid is equal to DEXKF .

Hence the area of a trapezoid is equal to its altitude ,

**multiplied**by the line whichjoins the middle points of the sides which are not parallel . PROPOSITION VIII .

Side 75

... ABC is to the triangle DEF as the square on BC is to B CE the square on EF .

By similar triangles , we have ( Def . 3 ) AB : DE :: : BC : EF . Alsn , BC : EF :: BC :

EF .

.

... ABC is to the triangle DEF as the square on BC is to B CE the square on EF .

By similar triangles , we have ( Def . 3 ) AB : DE :: : BC : EF . Alsn , BC : EF :: BC :

EF .

**Multiplying**together the corresponding terms of these pro portions , BOOK IV.

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### Vanlige uttrykk og setninger

ABCD altitude angle ABC angle ACB angle BAC base bisected called chord circle circumference coincide College common cone consequently construct contained convex surface curve described diagonals diameter difference distance divided draw drawn ellipse equal equivalent extremities faces fall figure formed four frustum given greater half hence hyperbola included inscribed intersect join less Loomis major axis manner Mathematics mean measured meet multiplied opposite ordinate parallel parallelogram parallelopiped pass perpendicular plane plane MN polygon prism PROBLEM Professor Prop proportional PROPOSITION proved pyramid radii radius ratio reason rectangle regular represent right angles Scholium segment sides similar solid sphere spherical square straight line tangent THEOREM third triangle ABC vertex vertices VIII whole

### Populære avsnitt

Side 60 - Any two rectangles are to each other as the products of their bases by their altitudes.

Side 17 - If two triangles have two sides, and the included angle of the one, equal to two sides and the included angle of the other, each to each, the two triangles will be equal, their third sides will be equal, and their other angles will be equal, each to each.

Side 101 - When you have proved that the three angles of every triangle are equal to two right angles...

Side 63 - 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 18 - BC common to the two triangles, which is adjacent to their equal angles ; therefore their other sides shall be equal, each to each, and the third angle of the one to the third angle of the other, (26.

Side 10 - When a straight line standing on another straight line makes the adjacent angles equal to one another, each of the angles is called a right angle ; and the straight line which stands on the other is called a perpendicular to it.

Side 32 - All the interior angles of any rectilineal figure, together with four right angles, are equal to twice as many right angles as the figure has sides.

Side 37 - Proportional, when the ratio of the first to the second is equal to the ratio of the second to the third.

Side 15 - Wherefore, when a straight line, &c. QED PROP. XIV. THEOR. If, at a point in a straight line, two other straight lines, upon the opposite sides of it, make the adjacent angles together equal to two right angles, these two straight lines shall be in one and the same straight line.

Side 44 - A Circle is a plane figure bounded by a curved line every point of which is equally distant from a point within called the center.