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 23.
Σελίδα 38
... alternate angles ÂEF , EFD , equal to one another . Then AB shall be parallel to CD . E D Construction . For , if AB be not parallel to CD , then AB and CD being produced will meet , either towards A and C , or towards B and D. Let AB ...
... alternate angles ÂEF , EFD , equal to one another . Then AB shall be parallel to CD . E D Construction . For , if AB be not parallel to CD , then AB and CD being produced will meet , either towards A and C , or towards B and D. Let AB ...
Σελίδα 39
... alternate angles ; therefore 3. AB is parallel to CD ( I. 27 ) . Wherefore , if a straight line , & c . Q.E.D. PROPOSITION 29. - Theorem . If a straight line fall upon two parallel straight lines , it makes the alternate angles equal to ...
... alternate angles ; therefore 3. AB is parallel to CD ( I. 27 ) . Wherefore , if a straight line , & c . Q.E.D. PROPOSITION 29. - Theorem . If a straight line fall upon two parallel straight lines , it makes the alternate angles equal to ...
Σελίδα 40
... alternate angles AGH , GHD shall be 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 , GHD upon the same side of EF ...
... alternate angles AGH , GHD shall be 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 , GHD upon the same side of EF ...
Σελίδα 41
... alternate angle GHF ( I. 29 ) . Again , because GHK cuts the parallel straight lines EF , CD in H , K , therefore 2. The exterior angle GHF is equal to the interior angle HKD , and it was shown that the angle AGH is equal to the angle ...
... alternate angle GHF ( I. 29 ) . Again , because GHK cuts the parallel straight lines EF , CD in H , K , therefore 2. The exterior angle GHF is equal to the interior angle HKD , and it was shown that the angle AGH is equal to the angle ...
Σελίδα 42
... alternate angles EAD , ADC equal to one another , therefore EF is parallel to BC ( I. 27 ) . Wherefore , through the given point A , a straight line EAF has been drawn parallel to the given straight line BC . Q.E.F. PROPOSITION 32 ...
... alternate angles EAD , ADC equal to one another , therefore EF is parallel to BC ( I. 27 ) . Wherefore , through the given point A , a straight line EAF has been drawn parallel to the given straight line BC . Q.E.F. PROPOSITION 32 ...
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.