The Elements of Euclid, containing the first six books, with a selection of geometrical problems. To which is added the parts of the eleventh and twelfth books which are usually read at the universities. By J. Martin1874 |
Αναζήτηση στο βιβλίο
Αποτελέσματα 11 - 15 από τα 85.
Σελίδα 25
... equal . Let the two straight lines AB , CD cut one another in the point E Then the angle AEC shall be equal to the ... angles CEA , AED . 1. The angles CEA , AED are together equal to two right angles ( I. 13 ) . Again , because ...
... equal . Let the two straight lines AB , CD cut one another in the point E Then the angle AEC shall be equal to the ... angles CEA , AED . 1. The angles CEA , AED are together equal to two right angles ( I. 13 ) . Again , because ...
Σελίδα 26
... angles . Let ABC be a triangle , and let the side BC be produced to D. Then the exterior angle ACD shall be greater ... equal to BE ( I. 3 ) and join FC . Demonstration . Because AE is equal to EC , and BE to EF ( constr . ) , and ...
... angles . Let ABC be a triangle , and let the side BC be produced to D. Then the exterior angle ACD shall be greater ... equal to BE ( I. 3 ) and join FC . Demonstration . Because AE is equal to EC , and BE to EF ( constr . ) , and ...
Σελίδα 35
... equal to it or less than it . If the angle BAC were equal to the angle EDF , then the base BC would be equal to the ... angles of the one equal to two angles of the other , each to each , and one side equal to one side - viz ...
... equal to it or less than it . If the angle BAC were equal to the angle EDF , then the base BC would be equal to the ... angles of the one equal to two angles of the other , each to each , and one side equal to one side - viz ...
Σελίδα 36
... angles ABC , BCA equal to the angles DEF , EFD , each to each , namely , ABC to DEF , and BCA to EFD ; also one side equal to one side . B E F First , let those sides be equal which are adjacent to the angles that are equal in the two ...
... angles ABC , BCA equal to the angles DEF , EFD , each to each , namely , ABC to DEF , and BCA to EFD ; also one side equal to one side . B E F First , let those sides be equal which are adjacent to the angles that are equal in the two ...
Σελίδα 37
... equal angles in each triangle be equal to one another , namely , AB equal to DE . Then in this case likewise , the other sides shall be equal , AC to DF , and BC to EF , and also the third angle BAC to the third angle EDF . B H E F ...
... equal angles in each triangle be equal to one another , namely , AB equal to DE . Then in this case likewise , the other sides shall be equal , AC to DF , and BC to EF , and also the third angle BAC to the third angle EDF . B H E F ...
Άλλες εκδόσεις - Προβολή όλων
The Elements of Euclid, Containing the First Six Books, with a Selection of ... Euclides Δεν υπάρχει διαθέσιμη προεπισκόπηση - 2016 |
Συχνά εμφανιζόμενοι όροι και φράσεις
AC is equal adjacent angles angle ABC angle ACB angle BAC angle BCD angle DEF angle EDF angle equal base BC bisected centre circle ABC circumference constr Demonstration diameter double equal angles equal to F equiangular equilateral triangle equimultiples ex æquali exterior angle fourth given circle given point given straight line gnomon greater ratio inscribed less Let ABC Let the straight linear units meet multiple opposite angle parallel to BC parallelogram perpendicular plane polygon produced proportionals Q.E.D. PROPOSITION quadrilateral rectangle contained remaining angle right angles segment semicircle similar square on AC straight line AB straight line BC straight line drawn three straight lines tiple touches the circle triangle ABC triangle DEF twice the rectangle wherefore
Δημοφιλή αποσπάσματα
Σελίδα 1 - 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.
Σελίδα 6 - 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 232 - If two triangles, which have two sides of the one proportional to two sides of the other, be joined at one angle, so as to have their homologous sides parallel to one another, the remaining sides shall be in a straight line. Let...
Σελίδα 112 - The angle in a semicircle is a right angle; the angle in a segment greater than a semicircle is less than a right angle; and the angle in a segment less than a semicircle is greater than a right angle.
Σελίδα 209 - ... triangles which have one angle in the one equal to one angle in the other, and their sides about the equal angles reciprocally proportional, are equal to one another.
Σελίδα 269 - 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. D c A' D' Hyp. In triangles ABC and A'B'C', ZA = ZA'. To prove AABC = ABxAC. A A'B'C' A'B'xA'C' Proof. Draw the altitudes BD and B'D'.
Σελίδα 199 - If two triangles have one angle of the one equal to one angle of the other and the sides about these equal angles proportional, the triangles are similar.
Σελίδα 23 - If two triangles have two angles of the one equal to two angles of the other, each to each, and also one side of the one equal to the corresponding side of the other, the triangles are congruent.
Σελίδα 63 - If a straight line be divided into two equal, and also into two unequal parts, the squares on the two unequal parts are together double of the square on half the line and of the square on the line between the points of section. Let the straight line AB be divided into two equal parts...
Σελίδα 32 - ... twice as many right angles as the figure has sides ; therefore all the angles of the figure together with four right angles, are equal to twice as many right angles as the figure has sides.