## Elements of Geometry and Conic Sections |

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Side 17

intersection , are together equal to four right angles . Cor . 2.

angles made by any number of straight lines meeting in one point , are together ...

**Hence**, if two straight lines cut one another , the four angles formed at the point ofintersection , are together equal to four right angles . Cor . 2.

**Hence**, all theangles made by any number of straight lines meeting in one point , are together ...

Side 19

3 ) ;

less than the sum of AB and AC ; and AC less than the sum of AB and BC

Therefore , any two sides , & c . PROPOSIT'ON IX . THEOREM . А If , from a point

withir a ...

3 ) ;

**hence**AB is less than the sum of AC and BC . For the same reason , BC isless than the sum of AB and AC ; and AC less than the sum of AB and BC

Therefore , any two sides , & c . PROPOSIT'ON IX . THEOREM . А If , from a point

withir a ...

Side 20

consequently , each of these angles is a right angle ( Def . 10 ) . Therefore , the

line bisecting the vertical angle of an isosceles triangle bisects the base at right ...

**Hence**, also , the line BD is equal to DC , and the angle ADB equal to ADC ;consequently , each of these angles is a right angle ( Def . 10 ) . Therefore , the

line bisecting the vertical angle of an isosceles triangle bisects the base at right ...

Side 21

XI . ) , which is contrary to the supposition . Neither is it less , because then the

side AB would be less than the side AC , according to the former part of this

proposition ;

& c .

XI . ) , which is contrary to the supposition . Neither is it less , because then the

side AB would be less than the side AC , according to the former part of this

proposition ;

**hence**ACB must be greater than ABC . Therefore , the greater side ,& c .

Side 23

which is also contrary to the hypothesis . Therefore , the angle A must be equal to

the angle D. In the same manner , it may be proved that the angle B is equal to

the angle E , and the angle C to the angle F ;

which is also contrary to the hypothesis . Therefore , the angle A must be equal to

the angle D. In the same manner , it may be proved that the angle B is equal to

the angle E , and the angle C to the angle F ;

**hence**the two triangles are equal .### Hva folk mener - Skriv en omtale

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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.