Elements of Plane Geometry: For the Use of SchoolsLewis & Sampson, 1844 - 96 σελίδες |
Αναζήτηση στο βιβλίο
Αποτελέσματα 1 - 5 από τα 22.
Σελίδα 13
... similar manner it may be shown that CEB - AED . PROP . IV . THEOREM . If two sides and the included angle , in one triangle , be respectively equal to the two sides and included an- gle in another triangle , these two triangles will be ...
... similar manner it may be shown that CEB - AED . PROP . IV . THEOREM . If two sides and the included angle , in one triangle , be respectively equal to the two sides and included an- gle in another triangle , these two triangles will be ...
Σελίδα 16
... similar manner it may be proved that BC cannot be longer than AC ; therefore they must be equal . Cor . Every equiangular triangle is equilateral . PROP . VIII . THEOREM . Two angles are equal when they have their sides par- allel and ...
... similar manner it may be proved that BC cannot be longer than AC ; therefore they must be equal . Cor . Every equiangular triangle is equilateral . PROP . VIII . THEOREM . Two angles are equal when they have their sides par- allel and ...
Σελίδα 21
... larger than C ; and ABC , which exceeds ABD , must be still larger than C. In a similar manner , if the side AC is taken longer than BC , may we prove the angle ABC to be larger than A. 22 SUM OF TWO SIDES OF TRIANGLES . [ BOOK 21 ...
... larger than C ; and ABC , which exceeds ABD , must be still larger than C. In a similar manner , if the side AC is taken longer than BC , may we prove the angle ABC to be larger than A. 22 SUM OF TWO SIDES OF TRIANGLES . [ BOOK 21 ...
Σελίδα 48
... similar , and the longest side , as above , must be opposite the given angle ( B. I. Prop . 15 ) . We will now consider the second of the above cases , In this case , if the side where the given angle is acute . opposite the given angle ...
... similar , and the longest side , as above , must be opposite the given angle ( B. I. Prop . 15 ) . We will now consider the second of the above cases , In this case , if the side where the given angle is acute . opposite the given angle ...
Σελίδα 55
... - bers , the products of the corresponding terms will be pro- portional . If and then will 2 : 3 :: 6 : 9 , 4:87 : 14 , 8 : 24 : 42 : 126 . LA BOOK V. DEFINITIONS . 1. Similar figures are those ,. BOOK IV . ] 55 PROPORTIONS .
... - bers , the products of the corresponding terms will be pro- portional . If and then will 2 : 3 :: 6 : 9 , 4:87 : 14 , 8 : 24 : 42 : 126 . LA BOOK V. DEFINITIONS . 1. Similar figures are those ,. BOOK IV . ] 55 PROPORTIONS .
Άλλες εκδόσεις - Προβολή όλων
Elements of Plane Geometry: For the Use of Schools - Primary Source Edition Nicholas Tillinghast Δεν υπάρχει διαθέσιμη προεπισκόπηση - 2013 |
Συχνά εμφανιζόμενοι όροι και φράσεις
ABCD adjacent angles allel alternate angles altitude angle ABC angles ABD angles is equal antecedent and consequent B. I. Ax base centre circle whose radius circumference circumscribed circumscribed circle Converse of Prop describe an arc diagonal diameter divide draw the line equal angles equal B. I. Prop equal chords equal Prop equal respectively equiangular equivalent feet given angle given line given point given side half hence the triangles hypotenuse included angle inscribed angle Let the triangles line drawn linear units longer than AC multiplied number of sides oblique lines parallel to CD parallelogram perimeter perpendicular PROBLEM prove radii rectangle regular polygons respectively equal right angles Prop right-angled triangle Scholium sides AC similar subtended tangent THEOREM three sides triangles ABC triangles are equal vertex
Δημοφιλή αποσπάσματα
Σελίδα 31 - 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.
Σελίδα 63 - The square described on the hypothenuse of a right-angled triangle is equivalent to the sum of the squares described on the other two sides.
Σελίδα 70 - The areas of two triangles which have an angle of the one equal to an angle of the other are to each other as the products of the sides including the equal angles. A D A' Hyp. In triangles ABC and A'B'C', To prove AABC A A'B'C' A'B' x A'C ' Proof. Draw the altitudes BD and B'D'.
Σελίδα 53 - In any proportion, the product of the means is equal to the product of the extremes.
Σελίδα 87 - The perimeters of two regular polygons of the same number of sides, are to each other as their homologous sides, and their areas are to each other as the squares of those sides (Prop.
Σελίδα 54 - In a series of equal ratios, any antecedent is to its consequent, as the sum of all the antecedents is to the sum of all the consequents. Let a: 6 = c: d = e :/. Then, by Art.
Σελίδα 81 - 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 59 - The area of a parallelogram is equal to the product of its base and its height: A = bx h.
Σελίδα 61 - From this proposition it is evident, that the square described on the difference of two lines is equivalent to the sum of the squares described on the lines respectively, minus twice the rectangle contained by the lines.
Σελίδα 82 - The side of a regular hexagon inscribed in a circle is equal to the radius of the circle.