Elements of Geometry with NotesCarey, Lea, & Blanchard, 1833 - 216 σελίδες |
Αναζήτηση στο βιβλίο
Αποτελέσματα 1 - 5 από τα 40.
Σελίδα 12
... equal ( Prop . VIII . ) , which is impossible ; therefore AB cannot be longer than AC , and in a similar man- ner it ... respectively to the two B СЕ F angles , E , F , and interjacent side EF in the other , the two triangles will be equal ...
... equal ( Prop . VIII . ) , which is impossible ; therefore AB cannot be longer than AC , and in a similar man- ner it ... respectively to the two B СЕ F angles , E , F , and interjacent side EF in the other , the two triangles will be equal ...
Σελίδα 13
... equal respectively to the two A sides KM , MC , and the included angle in the other ; hence the angle IBM is equal to the angle KCM ; ( Prop . VIII . ) ; but by hypothesis , the angle IBM is equal to the angle HCM ; therefore the angle ...
... equal respectively to the two A sides KM , MC , and the included angle in the other ; hence the angle IBM is equal to the angle KCM ; ( Prop . VIII . ) ; but by hypothesis , the angle IBM is equal to the angle HCM ; therefore the angle ...
Σελίδα 21
... equal , as we have already proved . Cor . 2. Hence , if from a point to a line two lines be drawn , then , that ... respectively equal to the hypothenuse and a side in the other . PROPOSITION XXIII . THEOREM . If two sides of one ...
... equal , as we have already proved . Cor . 2. Hence , if from a point to a line two lines be drawn , then , that ... respectively equal to the hypothenuse and a side in the other . PROPOSITION XXIII . THEOREM . If two sides of one ...
Σελίδα 22
... equal to DE , DF , and the included angle ( Prop . VIII ) ; consequently BC is longer than EF . PROPOSITION XXIV . THEOREM . ( Converse of Prop . XXIII . ) If two sides of one triangle be respectively equal to two sides of another ...
... equal to DE , DF , and the included angle ( Prop . VIII ) ; consequently BC is longer than EF . PROPOSITION XXIV . THEOREM . ( Converse of Prop . XXIII . ) If two sides of one triangle be respectively equal to two sides of another ...
Σελίδα 23
John Radford Young Michael Floy. PROPOSITION XXVI . THEOREM . Two triangles are equal , if two sides , and an opposite angle in one are respectively equal to two sides , and a corresponding opposite angle in the other ; provided the ...
John Radford Young Michael Floy. PROPOSITION XXVI . THEOREM . Two triangles are equal , if two sides , and an opposite angle in one are respectively equal to two sides , and a corresponding opposite angle in the other ; provided the ...
Άλλες εκδόσεις - Προβολή όλων
Συχνά εμφανιζόμενοι όροι και φράσεις
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
Δημοφιλή αποσπάσματα
Σελίδα 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.
Σελίδα 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...
Σελίδα 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...
Σελίδα 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...
Σελίδα 157 - To describe an isosceles triangle, having each of the angles at the base double of the third angle.
Σελίδα 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.
Σελίδα 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.
Σελίδα 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.
Σελίδα 196 - Now the parallelogram BL is double of the triangle ABD, because they are upon the same base BD, and between the same parallels...
Σελίδα 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.