Elements of Plane Geometry: For the Use of Schools |
From inside the book
Results 1-5 of 11
Page 9
... scholium is a remark subjoined to a demonstration . Axioms . 1. Things which are equal to the same thing , are equal to each other . 2. Things which are double , triple , & c . of the same or equal things , are equal to each other . 3 ...
... scholium is a remark subjoined to a demonstration . Axioms . 1. Things which are equal to the same thing , are equal to each other . 2. Things which are double , triple , & c . of the same or equal things , are equal to each other . 3 ...
Page 15
... Scholium . In a triangle any side may be assumed as the base , and then the vertex is the vertex of the oppo- site angle . In an isosceles triangle , however , we generally assume as the base the side which is not equal to either of the ...
... Scholium . In a triangle any side may be assumed as the base , and then the vertex is the vertex of the oppo- site angle . In an isosceles triangle , however , we generally assume as the base the side which is not equal to either of the ...
Page 27
... Scholium . The equal angles are opposite the equal sides . PROP . XXIII . THEOREM . If a straight line be so situated that of any two points in it each is equally distant from the extremities of another straight line , it will bisect ...
... Scholium . The equal angles are opposite the equal sides . PROP . XXIII . THEOREM . If a straight line be so situated that of any two points in it each is equally distant from the extremities of another straight line , it will bisect ...
Page 34
... the angles are unequal the chords will be unequal . Scholium . The above reasoning applies obviously to the case of equal circles , as one would entirely coincide with the other . PROP . IV . THEOREM . ( Converse of Prop 34 ...
... the angles are unequal the chords will be unequal . Scholium . The above reasoning applies obviously to the case of equal circles , as one would entirely coincide with the other . PROP . IV . THEOREM . ( Converse of Prop 34 ...
Page 49
... Scholium . If CD is not of sufficient length to reach the line FL , there will be no triangle which can be formed of the given parts ; if it touches FL without cutting it , there will be a right - angled triangle formed , and but one ...
... Scholium . If CD is not of sufficient length to reach the line FL , there will be no triangle which can be formed of the given parts ; if it touches FL without cutting it , there will be a right - angled triangle formed , and but one ...
Other editions - View all
Elements of Plane Geometry: For the Use of Schools - Primary Source Edition Nicholas Tillinghast No preview available - 2013 |
Common terms and phrases
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
Popular passages
Page 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.
Page 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.
Page 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'.
Page 53 - In any proportion, the product of the means is equal to the product of the extremes.
Page 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.
Page 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.
Page 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.
Page 59 - The area of a parallelogram is equal to the product of its base and its height: A = bx h.
Page 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.
Page 82 - The side of a regular hexagon inscribed in a circle is equal to the radius of the circle.