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
Σελίδα 13
... equal to AC , and let the equal sides AB , AC be produced to D and E. Then the angle ABC shall be equal to the angle ACB , and the angle DBC to the angle ECB . A F B 0 9 D E Construction . In BD take any point F ; and from AE the ...
... equal to AC , and let the equal sides AB , AC be produced to D and E. Then the angle ABC shall be equal to the angle ACB , and the angle DBC to the angle ECB . A F B 0 9 D E Construction . In BD take any point F ; and from AE the ...
Σελίδα 19
... angle . It is required to bisect it . Construction . In AB take any point D ; from AC cut off AED equal to ADE ( I . 3 ) , and join DE ; on the side of DE remote from A ... angle ACD is equal to the angle BOOK I. PROP . IX . 19.
... angle . It is required to bisect it . Construction . In AB take any point D ; from AC cut off AED equal to ADE ( I . 3 ) , and join DE ; on the side of DE remote from A ... angle ACD is equal to the angle BOOK I. PROP . IX . 19.
Σελίδα 32
... equal to the three given straight lines A , B , C. Q.E.F. PROPOSITION 23. - Problem . At a given point in a given straight line , to make a rectilineal angle equal to a given rectilineal angle . Let AB be the given straight line , and A ...
... equal to the three given straight lines A , B , C. Q.E.F. PROPOSITION 23. - Problem . At a given point in a given straight line , to make a rectilineal angle equal to a given rectilineal angle . Let AB be the given straight line , and A ...
Σελίδα 36
... equal to the angles DEF , EFD , each to each , namely , ABC to DEF , and BCA to EFD ; also one side equal to one ... angle BAC to the third angle EDF . Construction . For , if AB be not equal to DE , one of them must be greater ...
... equal to the angles DEF , EFD , each to each , namely , ABC to DEF , and BCA to EFD ; also one side equal to one ... angle BAC to the third angle EDF . Construction . For , if AB be not equal to DE , one of them must be greater ...
Σελίδα 40
... equal to one another ; the exterior angle EGB shall be equal to the interior and opposite angle GHD upon the same side of the line EF ; and the two interior angles BGH , ĠHD upon the ... angle EGB is equal to the 40 EUCLID'S ELEMENTS .
... equal to one another ; the exterior angle EGB shall be equal to the interior and opposite angle GHD upon the same side of the line EF ; and the two interior angles BGH , ĠHD upon the ... angle EGB is equal to the 40 EUCLID'S ELEMENTS .
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
AB is equal 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 draw equal angles equal to F equiangular equilateral triangle equimultiples exterior angle given circle given point given straight line gnomon greater ratio inscribed less Let ABC Let the straight meet multiple opposite angle parallel to BC parallelogram perpendicular plane polygon produced proportionals PROPOSITION 13 Q.E.D. PROPOSITION rectangle contained remaining angle right angles segment similar square on AC straight line AB straight line BC straight line drawn Theorem 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.