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 |
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Αποτελέσματα 1 - 5 από τα 89.
Σελίδα 13
... join FC , GB . Demonstration . Because AF is equal to AG ( constr . ) , and AB to AC ( hyp . ) ; the two sides FA , AC are equal to the two GA , AB , each to each , and they contain the angle FÂG common to the two tri- angles AFC , AGB ...
... join FC , GB . Demonstration . Because AF is equal to AG ( constr . ) , and AB to AC ( hyp . ) ; the two sides FA , AC are equal to the two GA , AB , each to each , and they contain the angle FÂG common to the two tri- angles AFC , AGB ...
Σελίδα 14
... cut off BD equal to CA the less ( I. 3 ) , and join DC . * An abbreviation for quod erat demonstrandum — that is , " which was to be demonstrated or proved . ' Demonstration . Then , in the triangles DBC , ABC 14 EUCLID'S ELEMENTS .
... cut off BD equal to CA the less ( I. 3 ) , and join DC . * An abbreviation for quod erat demonstrandum — that is , " which was to be demonstrated or proved . ' Demonstration . Then , in the triangles DBC , ABC 14 EUCLID'S ELEMENTS .
Σελίδα 16
... Join CD . Demonstration . Because AC is equal to AD in the triangle ACD ; therefore , 1. The angle ACD is equal to the angle ADC ( I. 5 ) . But the angle ACD is greater than the angle BCD ( Ax . 9 ) ; there- fore also 2. The angle ADC ...
... Join CD . Demonstration . Because AC is equal to AD in the triangle ACD ; therefore , 1. The angle ACD is equal to the angle ADC ( I. 5 ) . But the angle ACD is greater than the angle BCD ( Ax . 9 ) ; there- fore also 2. The angle ADC ...
Σελίδα 17
... join CD . Demonstration . Then , because AC is equal to AD in the tri- angle ACD , the angles upon the other side of the base CD , namely , 1. The angles ECD , FDC are equal to one another ( I. 5 ) ; but the angle ECD is greater than ...
... join CD . Demonstration . Then , because AC is equal to AD in the tri- angle ACD , the angles upon the other side of the base CD , namely , 1. The angles ECD , FDC are equal to one another ( I. 5 ) ; but the angle ECD is greater than ...
Σελίδα 19
... join DE ; on the side of DE remote from A , describe the equilateral triangle DEF ( I. 1 ) , and join AF . Then the straight line AF shall bisect the angle BAC , Proof . Because AD is equal to AE ( constr . ) , and AF is common to the ...
... join DE ; on the side of DE remote from A , describe the equilateral triangle DEF ( I. 1 ) , and join AF . Then the straight line AF shall bisect the angle BAC , Proof . Because AD is equal to AE ( constr . ) , and AF is common to the ...
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.