Pure mathematics, Τόμος 11874 |
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Σελίδα 96
... bases , or third sides , equal ; and the two triangles shall be equal , and their other angles shall be equal , each to each ... base EF ; The triangle ABC shall be equal to the triangle DEF ; * Q. E. F. is an abbreviation for quod erat ...
... bases , or third sides , equal ; and the two triangles shall be equal , and their other angles shall be equal , each to each ... base EF ; The triangle ABC shall be equal to the triangle DEF ; * Q. E. F. is an abbreviation for quod erat ...
Σελίδα 97
... base BC shall coincide with the base EF . Because the point B coinciding with E , and C with F , if the base BC do not coincide with the base EF , two straight lines would enclose a space , which is impossible ( Ax . 10 ) . Therefore the ...
... base BC shall coincide with the base EF . Because the point B coinciding with E , and C with F , if the base BC do not coincide with the base EF , two straight lines would enclose a space , which is impossible ( Ax . 10 ) . Therefore the ...
Σελίδα 98
... base ) . FA , AC re- spectively = GA , AB . F ..FC = GB and AFC = A AGB . LACF = 4 ABG . LAFC = L AGB . BF = CG ... base FC is equal to the base GB ( I. 4 ) ; And the triangle AFC to the triangle AGB ( I. 4 ) ; And the remaining angles ...
... base ) . FA , AC re- spectively = GA , AB . F ..FC = GB and AFC = A AGB . LACF = 4 ABG . LAFC = L AGB . BF = CG ... base FC is equal to the base GB ( I. 4 ) ; And the triangle AFC to the triangle AGB ( I. 4 ) ; And the remaining angles ...
Σελίδα 99
... base DC is equal to the base AB ( I. 4 ) . And the triangle DBC is equal to the tri- angle ACB ( I. 4 ) , the less to the greater , which is absurd . B D DB = AC . CA DBC = Therefore AB is not unequal to AC , that is , it is equal to it ...
... base DC is equal to the base AB ( I. 4 ) . And the triangle DBC is equal to the tri- angle ACB ( I. 4 ) , the less to the greater , which is absurd . B D DB = AC . CA DBC = Therefore AB is not unequal to AC , that is , it is equal to it ...
Σελίδα 100
... base , and on the same side of it , there cannot be two triangles that have their sides , which are terminated in one extremity of the base , equal to one another , and likewise those which are terminated in the other extremity . Let ...
... base , and on the same side of it , there cannot be two triangles that have their sides , which are terminated in one extremity of the base , equal to one another , and likewise those which are terminated in the other extremity . Let ...
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Συχνά εμφανιζόμενοι όροι και φράσεις
a²b a²b² a²x² a³b ab² ab³ ABCD adjacent angles algebraical algebraical quantity angle ABC angle BAC angle BCD angle EDF angle equal base BC BC is equal bisect brackets cent centim centre circle ABC coefficient common Const cube root decimal figures denominator distance divided divisor equation expression exterior angle factor Find the value fraction given rectilineal given straight line greater Hence join kilom Let ABC logarithm metres millig Multiply opposite angles parallel parallelogram perpendicular PROOF.-Because Q. E. D. Proposition quotient ratio rectangle contained remainder right angles segment side BC square on AC square root subtraction term triangle ABC x²y x²y² x³y xy² xy³
Δημοφιλή αποσπάσματα
Σελίδα 116 - Wherefore, if a straight line, &c. QED PROPOSITION XXVIII. THEOREM. If a straight line falling upon two other straight lines, make the exterior angle equal to...
Σελίδα 103 - When a straight line standing on another straight line makes the adjacent angles equal to one another, each of the angles is called a right angle; and the straight line which stands on the other is called a perpendicular to it.
Σελίδα 113 - 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...
Σελίδα 88 - 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 : 16.
Σελίδα 273 - The opposite angles of any quadrilateral figure inscribed in a circle, are together equal to two right angles.
Σελίδα 94 - J which the equal sides are opposite, shall be equal, each to each, viz. the angle ABC to the angle DEF, and the angle ACB to DFE.
Σελίδα 271 - If a straight line touch a circle, and from the point of contact a straight line be drawn cutting the circle ; the angles which this line makes with the line touching the circle, shall be equal to the angles which are in the alternate segments of the circle.
Σελίδα 91 - If a straight line meets 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 112 - IMS the greater base shall be greater t/uin the angle contained by the sides equal to them of the other. Let ABC, DEF, be two triangles, which have The two sides AB, AC...
Σελίδα 128 - To a given straight line to apply a parallelogram, which shall be equal to a given triangle, and have one of its angles equal to a given rectilineal angle.