An introduction to geometry, consisting of Euclid's Elements, book i, accompanied by numerous explanations, questions, and exercises, by J. Walmsley. [With] Answers, Τόμος 11884 |
Αναζήτηση στο βιβλίο
Αποτελέσματα 1 - 5 από τα 17.
Σελίδα 34
... angle CBE from the angle ABE , and BCD from ACD ; and state the remainders . 18. If ABE , ACD be equal , and also CBE , BCD , what will follow with regard to the two remainders ? 31. PROPOSITION V. - THEOREM . The angles at the base of ...
... angle CBE from the angle ABE , and BCD from ACD ; and state the remainders . 18. If ABE , ACD be equal , and also CBE , BCD , what will follow with regard to the two remainders ? 31. PROPOSITION V. - THEOREM . The angles at the base of ...
Σελίδα 37
... angle DBC of the triangle DCB are respectively equal to AC , CB , and the angle ACB of the triangle ACB ; then , by Prop ... BCD , BCA , BDC , ADC . What angles are both subtended by CD ? 34. PROPOSITION VI . THeorem . If two angles of a ...
... angle DBC of the triangle DCB are respectively equal to AC , CB , and the angle ACB of the triangle ACB ; then , by Prop ... BCD , BCA , BDC , ADC . What angles are both subtended by CD ? 34. PROPOSITION VI . THeorem . If two angles of a ...
Σελίδα 41
... angle DCB is greater than DBC . 12. Prove that ABC and DBC in the figure cannot both be isosceles triangles . E B B 13. In the annexed figure , having A and Don opposite sides of BC , let ABC be isosceles ; then prove that the angle BCD ...
... angle DCB is greater than DBC . 12. Prove that ABC and DBC in the figure cannot both be isosceles triangles . E B B 13. In the annexed figure , having A and Don opposite sides of BC , let ABC be isosceles ; then prove that the angle BCD ...
Σελίδα 42
... angle ADC is equal to the angle ACD ; ( I. 5 ) but the angle ACD is greater than the angle BCD ; ( Ax . 9 ) therefore ADC is also greater than BCD ; even more , then , is the angle BDC greater than BCD . ( Ax . 9 ) Again , in the ...
... angle ADC is equal to the angle ACD ; ( I. 5 ) but the angle ACD is greater than the angle BCD ; ( Ax . 9 ) therefore ADC is also greater than BCD ; even more , then , is the angle BDC greater than BCD . ( Ax . 9 ) Again , in the ...
Σελίδα 43
... angle ECD is greater than the angle BCD ; ( Ax . 9 ) therefore also FDC is greater than BCD ; Even more , then , is the angle BDC greater than BCD . ( Ax.9 ) Again , in the triangle BCD , BD is equal to BC , therefore the angle BDC is ...
... angle ECD is greater than the angle BCD ; ( Ax . 9 ) therefore also FDC is greater than BCD ; Even more , then , is the angle BDC greater than BCD . ( Ax.9 ) Again , in the triangle BCD , BD is equal to BC , therefore the angle BDC is ...
Άλλες εκδόσεις - Προβολή όλων
An Introduction to Geometry, Consisting of Euclid's Elements, Book I ... Euclides Δεν υπάρχει διαθέσιμη προεπισκόπηση - 2013 |
An Introduction to Geometry, Consisting of Euclid's Elements, Book I ... Euclides Δεν υπάρχει διαθέσιμη προεπισκόπηση - 2023 |
An Introduction to Geometry, Consisting of Euclid's Elements, Book I ... Euclides Δεν υπάρχει διαθέσιμη προεπισκόπηση - 2018 |
Συχνά εμφανιζόμενοι όροι και φράσεις
AB is equal AC is equal adjacent angles alternate angle angle ABC angle ACB angle AGH angle BAC angle BCD angle equal angles CBA axiom base BC bisects the angle centre circle circumference Constr construction definition describe diagonal Diagram diameter enunciation equal and parallel equal angles equal sides equal to BC EQUIANGULAR POLYGONS equilateral triangle Euclid Euclid's Elements exterior four right angles Geometry given angle given point given straight line greater hypotenuse hypothesis inference isosceles triangle join less Let ABC magnitude meet middle point opposite angles opposite interior angle opposite sides pair of equal parallel to BC parallelogram perpendicular Postulate produced proof Prop proposition prove quadrilateral rectilineal figure respectively equal rhombus right angles right-angled triangle sides equal square supplementary angles theorems thesis trapezium triangle ABC triangles are equal unequal vertex Wherefore
Δημοφιλή αποσπάσματα
Σελίδα 132 - To a given straight line to apply a parallelogram, which shall be equal to a given triangle, and have one of its angles equal to a given rectilineal angle.
Σελίδα 86 - All the interior angles of any rectilineal figure, together with four right angles, are equal to twice as many right angles as the figure has sides.
Σελίδα 139 - 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 133 - The complements of the parallelograms, which are about the diameter of any parallelogram, are equal to one another.
Σελίδα 134 - Prove that parallelograms on the same base and between the same parallels are equal in area.
Σελίδα 134 - To draw a straight line through a given point parallel to a given straight line. Let A be the given point, and BC the given straight line ; it is required to draw a straight line through the point A, parallel to the straight hue BC.
Σελίδα 50 - if two straight lines" &c. QED COR. 1. From this it is manifest, that if two straight lines cut one another, the angles which they make at the point where they cut, are together equal to four right angles.
Σελίδα 20 - PROB. from a given point to draw a straight line equal to a given straight line. Let A be the given point, and BC the given straight line : it is required to draw from the point A a straight line equal to BC.
Σελίδα 96 - Parallelograms upon the same base and between the same parallels, are equal to one another.
Σελίδα 49 - If at a point in a straight line, two other straight lines, upon the opposite sides of it, make the adjacent angles together equal to two right angles ; then these two straight lines shall be in one and the same straight line.