## Elements of Geometry and Conic Sections |

### Inni boken

Resultat 1-5 av 9

Side 18

... and the included side of the one , equal to two angles and the included side of

the other , each to each , the two triangles will be equal , the other sides will be

equal , each to each , and the

.

... and the included side of the one , equal to two angles and the included side of

the other , each to each , the two triangles will be equal , the other sides will be

equal , each to each , and the

**third**angle of the one to the**third**angle of the other.

Side 37

Thus , if A has to B the same ratio that C has to D , these för quantities form a

proportion , and we write it А с BD ' A : B :: C : D . The first and last terms of a

proportion are called the two extremes , and the second and

means .

Thus , if A has to B the same ratio that C has to D , these för quantities form a

proportion , and we write it А с BD ' A : B :: C : D . The first and last terms of a

proportion are called the two extremes , and the second and

**third**terms the twomeans .

Side 67

The right - angled triangle is the only one in which the sum of the squares of two

sides is equivalent to the square on the

the two sides is acute , the sum of their squares is greater than the square of the ...

The right - angled triangle is the only one in which the sum of the squares of two

sides is equivalent to the square on the

**third**side ; for , if the angle contained bythe two sides is acute , the sum of their squares is greater than the square of the ...

Side 87

PROBLEM IX . Given one side and two angles of a triangle , to construct the

triangle . DY The two given angles will either be both adjacent to the given side ,

or one adjacent and the other opposite . In the latter case , find the

Prob .

PROBLEM IX . Given one side and two angles of a triangle , to construct the

triangle . DY The two given angles will either be both adjacent to the given side ,

or one adjacent and the other opposite . In the latter case , find the

**third**angle (Prob .

Side 143

For the same reason , the

prism hik - e are equivalent ; the fourth exterior and the

to the last in each series . Hence all the exterior prisms of the pyramid A - BCD ...

For the same reason , the

**third**exterior prism HIK - L and the second interiorprism hik - e are equivalent ; the fourth exterior and the

**third**interior ; and so on ,to the last in each series . Hence all the exterior prisms of the pyramid A - BCD ...

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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.