The elements of plane geometry, Volum 1 |
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Side 101
... altitude of a parallelogram with reference to a given side as base is the perpendicular distance between the base and the opposite side . DEF 2. The altitude of a triangle with reference to a given side as base is the perpendicular ...
... altitude of a parallelogram with reference to a given side as base is the perpendicular distance between the base and the opposite side . DEF 2. The altitude of a triangle with reference to a given side as base is the perpendicular ...
Side 102
... altitude , and by I. 30 , Cor . , this rectangle is equal to any other rectangle whose base and altitude are respectively equal to those of the other . COR . 2. Parallelograms on equal bases and of equal altitudes are equal ; and of ...
... altitude , and by I. 30 , Cor . , this rectangle is equal to any other rectangle whose base and altitude are respectively equal to those of the other . COR . 2. Parallelograms on equal bases and of equal altitudes are equal ; and of ...
Side 103
... altitude . Parallelograms on equal bases and of equal altitudes are equal , since each parallelogram is equal to a rectangle whose base and altitude are equal to those of the parallelogram . Again , rectangles of equal altitudes but on ...
... altitude . Parallelograms on equal bases and of equal altitudes are equal , since each parallelogram is equal to a rectangle whose base and altitude are equal to those of the parallelogram . Again , rectangles of equal altitudes but on ...
Side 104
... altitudes are equal . For each triangle is half a rectangle whose base and altitude are equal to those of the triangles , and such rectangles are equal by I. 30 , Cor . COR . 2. Equal triangles on the same or equal bases have equal alti ...
... altitudes are equal . For each triangle is half a rectangle whose base and altitude are equal to those of the triangles , and such rectangles are equal by I. 30 , Cor . COR . 2. Equal triangles on the same or equal bases have equal alti ...
Side 105
... altitude being greater than the other , so is the triangle of greater altitude greater than the other . Hence , by contraposition , if the triangles are equal their altitudes are also equal . COR . 3. If two equal triangles stand on the ...
... altitude being greater than the other , so is the triangle of greater altitude greater than the other . Hence , by contraposition , if the triangles are equal their altitudes are also equal . COR . 3. If two equal triangles stand on the ...
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Vanlige uttrykk og setninger
AB is equal ABCD AC is equal adjacent angles adjoining sides alternate angle angle ABC angle ACB angle AFG angle BAC angle CAB angle DEF angle EDF angle FGD angles are equal angles equal BA and AC base BC bisector bisects centre circle cutting Constr construct a triangle contrapositive diagonal distance draw a circle equal angles equal to AC equal to CD exterior angle find the locus Geometry given angle given point given straight line greater Hence hypotenuse identically equal interior opposite angle isosceles triangle less Let ABC meet middle point obtuse angle opposite sides parallel straight lines parallelogram perpendicular point equidistant Prob produced quadrilateral rectangle contained rectangle whose base right angles right-angled triangle shew side AB side AC sides equal square on AC squares on AB straight line drawn Theorem trapezium triangle ABC triangles are identically twice the rectangle vertex
Populære avsnitt
Side 27 - If two triangles have two angles of the one equal to two angles of the other, each to each, and one side equal to one side, viz. either the sides adjacent to the equal...
Side 98 - A circle is a plane figure contained by one line, which is called the circumference, and is such that all straight lines drawn from a certain point within the figure to the circumference, are equal to one another.
Side 35 - Any two sides of a triangle are together greater than the third side.
Side 26 - The straight lines drawn from the extremities of the base of an isosceles triangle to the middle points of the opposite sides are equal to one another.
Side 37 - Of all the straight lines that can be drawn to a given straight line from a given point outside it, the perpendicular is the shortest.
Side 70 - A diameter of a circle is a straight line drawn through the centre, and terminated both ways by the circumference.
Side 110 - Iff a straight line be divided into any two parts, four times the rectangle contained by the whole line, and one of the parts, together with the square of the other part, is equal to the square of the straight line which is made up of the whole and that part.
Side 31 - Any two angles of a triangle are together less than two right angles.
Side 115 - In a right.angled triangle, the square on the hypotenuse is equal to the sum of the squares on the sides containing the right angle . . . . 130 Applications of Pythagoras' theorem . . . . 132 THEOREM 6.