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 6 - 10 από τα 86.
Σελίδα 16
... Construction . 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 ...
... Construction . 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 ...
Σελίδα 19
... Construction . In AB take any point ; from AC cut off AED equal to ARE ( I . 3 ) , and 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 ...
... Construction . In AB take any point ; from AC cut off AED equal to ARE ( I . 3 ) , and 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 ...
Σελίδα 20
... Construction . In AC take any point D , and make CE equal to CD ( I. 3 ) ; upon DE describe the equilateral triangle DEF ( I. 1 ) , and join CF. Then CF , drawn from the point C , shall be at right angles to AB . Proof . Because DC is ...
... Construction . In AC take any point D , and make CE equal to CD ( I. 3 ) ; upon DE describe the equilateral triangle DEF ( I. 1 ) , and join CF. Then CF , drawn from the point C , shall be at right angles to AB . Proof . Because DC is ...
Σελίδα 23
... Construction . From the point B draw BE at right angles to CD ( I. 11 ) . Demonstration . Because BE is at right angles to CD ( constr . ) , therefore 1. The angles CBE , EBD are two right angles ( Def . 10 ) . And because the angle CBE ...
... Construction . From the point B draw BE at right angles to CD ( I. 11 ) . Demonstration . Because BE is at right angles to CD ( constr . ) , therefore 1. The angles CBE , EBD are two right angles ( Def . 10 ) . And because the angle CBE ...
Σελίδα 26
... Construction . Bisect AC in E ( I. 10 ) , and join BE ; produce BE to F , making EF equal to BE ( I. 3 ) and join FC . Demonstration . Because AE is equal to EC , and BE to EF ( constr . ) , and 1. The two sides AE , EB are equal to the ...
... Construction . Bisect AC in E ( I. 10 ) , and join BE ; produce BE to F , making EF equal to BE ( I. 3 ) and join FC . Demonstration . Because AE is equal to EC , and BE to EF ( constr . ) , and 1. The two sides AE , EB are equal 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.