## Elements of Geometry and Conic Sections |

### Inni boken

Resultat 1-5 av 84

Side 6

Several of Legendre's

, while some of his corollaries ... his recitation with the enunciation of the

As the ...

Several of Legendre's

**propositions**have been degraded to the rank of corollaries, while some of his corollaries ... his recitation with the enunciation of the

**proposition**, the leading words are repeated at the close of each demonstration .As the ...

Side 7

205 N.B. — When reference is made to a

number of the

different Book , the number of the Book is also specified . ELEMENTS OF

GEOMETRY ...

205 N.B. — When reference is made to a

**Proposition**in the same Book , only thenumber of the

**Proposition**is given ; but when the**Proposition**is found in adifferent Book , the number of the Book is also specified . ELEMENTS OF

GEOMETRY ...

Side 12

One

made the supposition in the second . 26. A corollary is an obvious consequence ,

resulting from one or more

...

One

**proposition**is the converse of another , when the conclusion of the first ismade the supposition in the second . 26. A corollary is an obvious consequence ,

resulting from one or more

**propositions**. 27. A scholium is a remark appended to...

Side 14

A G Le ; the straight line CD be perpendicular to AB , and GH to EF ; then , by

definition 10 , each of the angles ACD , BCD , EGH , FGH , will BE be a right

angle ...

**PROPOSITION**I. THEOREM . All right angles are equal to each other . D K к H нA G Le ; the straight line CD be perpendicular to AB , and GH to EF ; then , by

definition 10 , each of the angles ACD , BCD , EGH , FGH , will BE be a right

angle ...

Side 16

Therefore , if at a point , & c . may

straight lines , which have two points common , coincide with each other

throughout their whole extent , and form but one and the same straight line . Let

there be two ...

Therefore , if at a point , & c . may

**PROPOSITION**IV . THEOREM . C D Twostraight lines , which have two points common , coincide with each other

throughout their whole extent , and form but one and the same straight line . Let

there be two ...

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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.