Elements of Geometry with NotesCarey, Lea, & Blanchard, 1833 - 216 sider |
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Resultat 1-5 av 37
Side 3
... number of its sides . The boundary of the figure is called its perimeter . 13. Among polygons , however , are more particularly dis- tinguished the figure of three sides , called a triangle , and that of four sides called a ...
... number of its sides . The boundary of the figure is called its perimeter . 13. Among polygons , however , are more particularly dis- tinguished the figure of three sides , called a triangle , and that of four sides called a ...
Side 10
... number of straight lines in the same point is equal to four right angles , since they are only so many subdivisions ... sides , and the included angle in one triangle be equal to two sides , and the included angle in another triangle ...
... number of straight lines in the same point is equal to four right angles , since they are only so many subdivisions ... sides , and the included angle in one triangle be equal to two sides , and the included angle in another triangle ...
Side 66
... side of the other : join BC , which will be the side of the proposed square , as is evident from Prop . X. B. II . Scholium . A B Any number of squares may be reduced to a single one , by re- ducing two into one , this and a third into ...
... side of the other : join BC , which will be the side of the proposed square , as is evident from Prop . X. B. II . Scholium . A B Any number of squares may be reduced to a single one , by re- ducing two into one , this and a third into ...
Side 71
... sides of the square are tangents to the circle ( Prop . IX . B. III ... number of times without leaving a remainder , it is called a multi- ple of ... number of times . 5. And like submultiples are those which are contained in their ...
... sides of the square are tangents to the circle ( Prop . IX . B. III ... number of times without leaving a remainder , it is called a multi- ple of ... number of times . 5. And like submultiples are those which are contained in their ...
Side 90
... number of parallels be drawn , the sides will be cut proportionally , the opposite intercepted portions being to each other as the sides themselves . Scholium . The converse of this proposition does not follow , that is , it is not true ...
... number of parallels be drawn , the sides will be cut proportionally , the opposite intercepted portions being to each other as the sides themselves . Scholium . The converse of this proposition does not follow , that is , it is not true ...
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Vanlige uttrykk og setninger
AB² ABCD adjacent angles altitude angle ABC angle ACB angle BAC antecedent base bisected centre chord circle circum circumference circumscribed circles circumscribed polygon consequently construction Converse of Prop corollary demonstration described diagonals diameter divided draw equal angles equal Prop equiangular equimultiples equivalent Euclid exterior angle geometry greater half hence hypothenuse hypothesis included angle inscribed angle inscribed polygon intersect isosceles triangle join less line drawn lines be drawn magnitudes multiple number of sides obtuse opposite angles parallel perimeter perpendicular PROBLEM proportion PROPOSITION PROPOSITION VIII quadrilateral radii radius rectangle rectangle contained regular polygon respectively equal rhomboid right angled triangle right angles Prop Scholium scribed side BC similar polygons similar triangles square submultiple subtended surface tangent THEOREM third three angles trapezium triangle ABC vertex whence
Populære avsnitt
Side 177 - ... if a straight line, &c. QED PROPOSITION 29. — Theorem. If a straight line fall upon two parallel straight lines, it makes the alternate angles equal to one another ; and the exterior angle equal to the interior and opposite upon the same side ; and likewise the two interior angles upon the same side together equal to two right angles.
Side 184 - If a straight line meet two straight lines, so as to make the two interior angles on the same side of it taken together less than two right angles...
Side 31 - If there be two straight lines, one of which is divided into any number of parts, the rectangle contained by the two straight lines is equal to the rectangles contained by the undivided line, and the several parts of the divided line. Let...
Side 89 - IF a straight line be drawn parallel to one of the sides of a triangle, it shall cut the other sides, or those produced, proportionally; and if the sides, or the sides produced, be cut proportionally, the straight line which joins the points of section shall be parallel to the remaining side of the triangle...
Side 157 - To describe an isosceles triangle, having each of the angles at the base double of the third angle.
Side 24 - The difference of the angles at the base of any triangle, is double the angle contained by a line drawn from the vertex perpendicular to the base, and another bisecting the angle at the vertex.
Side 16 - 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 213 - We have already said that by the term convex line we understand a line, polygonal, or curve, or partly curve and . partly polygonal, such that a straight line cannot cut it in more than two points.
Side 196 - Now the parallelogram BL is double of the triangle ABD, because they are upon the same base BD, and between the same parallels...
Side 37 - In any triangle, the square of a side opposite an acute angle is equal to the sum of the squares of the other two sides diminished by twice the product of one of those sides and the projection of the other side upon it.