Elements of Geometry |
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Αποτελέσματα 6 - 10 από τα 46.
Σελίδα 11
The two oblique lines AC , AE , which meet the line DE on opposite sides of the
perpendicular , and at equal distances BC , BE , from it , are equal to one another
; . 3. Of any two oblique lines AC , AD , or AE , AD , that which is more remote ...
The two oblique lines AC , AE , which meet the line DE on opposite sides of the
perpendicular , and at equal distances BC , BE , from it , are equal to one another
; . 3. Of any two oblique lines AC , AD , or AE , AD , that which is more remote ...
Σελίδα 15
Since the angle AEK is a right angle , AE is a perpendicular , and consequently
less than the oblique line , AK ; whence in the triangle AEK the angle AKE ,
opposite to the side AE , is less than the right angle AEK , opposite to the side AK
( 49 ) ...
Since the angle AEK is a right angle , AE is a perpendicular , and consequently
less than the oblique line , AK ; whence in the triangle AEK the angle AKE ,
opposite to the side AE , is less than the right angle AEK , opposite to the side AK
( 49 ) ...
Σελίδα 19
41 ) the exterior Fig.41 , angle BAD is equal to the two opposite interior angles B
and C ' ; for , AE being parallel to BC , the part BAE is equal to the angle B , and
the other part DAE is equal to the angle C ( 67 ) . THEOREM . 79. The sum of all ...
41 ) the exterior Fig.41 , angle BAD is equal to the two opposite interior angles B
and C ' ; for , AE being parallel to BC , the part BAE is equal to the angle B , and
the other part DAE is equal to the angle C ( 67 ) . THEOREM . 79. The sum of all ...
Σελίδα 20
The opposite sides of a parallelogram are equal , and the opposite angles also
are equal . Demonstration . Draw the diagonal BD ( fig . 44 ) ; the two triangles
ADB , DBC , have the side BD common ; moreover , on account of the parallels
AD ...
The opposite sides of a parallelogram are equal , and the opposite angles also
are equal . Demonstration . Draw the diagonal BD ( fig . 44 ) ; the two triangles
ADB , DBC , have the side BD common ; moreover , on account of the parallels
AD ...
Σελίδα 21
THEOREM . sides of the other , each to each , they are therefore equal , and the
angle ADB opposite to the side AB is equal to the angle DBC opposite to the side
CD ; consequently the side AD is parallel to BC ( 67 ) . For a similar reason AB is
...
THEOREM . sides of the other , each to each , they are therefore equal , and the
angle ADB opposite to the side AB is equal to the angle DBC opposite to the side
CD ; consequently the side AD is parallel to BC ( 67 ) . For a similar reason AB is
...
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Συχνά εμφανιζόμενοι όροι και φράσεις
ABCD adjacent altitude angle ACB applied base called centre chord circ circle circumference circumscribed common comprehended cone consequently considered construction contained Corollary cylinder Demonstration described diameter difference distance divided draw drawn entire equal equivalent example extremities faces figure follows formed four give given greater half hence homologous sides inclination inscribed join less let fall manner mean measure meet moreover multiplied namely opposite parallel parallelogram parallelopiped pass perimeter perpendicular plane plane angles pole polyedron polygon prism PROBLEM proportional proposition pyramid radii radius ratio reason rectangle regular polygon remain respect right angles Scholium sector segment side BC similar solid angle Solution sphere spherical triangle square straight line suppose surface taken THEOREM third triangle ABC vertex vertices whence
Δημοφιλή αποσπάσματα
Σελίδα ii - Co. of the said district, have deposited in this office the title of a book, the right whereof they claim as proprietors, in the words following, to wit : " Tadeuskund, the Last King of the Lenape. An Historical Tale." In conformity to the Act of the Congress of the United States...
Σελίδα 9 - If two triangles have the three sides of the one equal to the three sides of the other, each to each, the triangles are congruent.
Σελίδα 63 - The square of the hypothenuse is equal to the sum of the squares of the other two sides ; as, 5033 402+302.
Σελίδα 9 - Hence a straight line drawn from the vertex of an isosceles triangle, to the middle of the base, is perpendicular to that base, and divides the vertical angle into two equal parts.
Σελίδα ii - States entitled an act for the encouragement of learning hy securing the copies of maps, charts and books to the author., and proprietors of such copies during the times therein mentioned, and also to an act entitled an act supplementary to an act, entitled an act for the encouragement of learning by securing the copies of maps, charts and books to the authors and proprietors of such copies during the times therein mentioned and extending the benefits thereof to the arts of designing, engraving and...
Σελίδα 61 - 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. A D A' Hyp. In triangles ABC and A'B'C', To prove AABC A A'B'C' A'B' x A'C ' Proof. Draw the altitudes BD and B'D'.
Σελίδα 166 - In any spherical triangle, the greater side is opposite the greater angle ; and conversely, the greater angle is opposite the greater side.
Σελίδα 153 - CIRCLE is a plane figure bounded by a curved line, all the points of which are equally distant from a point within called the centre; as the figure ADB E.
Σελίδα 25 - Two equal chords are equally distant from the centre ; and of two unequal chords, the less is at the greater distance from the centre.
Σελίδα 164 - If two triangles have two sides and the inchtded angle of the one respectively equal to two sides and the included angle of the other, the two triangles are equal in all respects.
Πληροφορίες βιβλιογραφίας
| Τίτλος | Elements of Geometry |
| Συγγραφέας | Adrien Marie Legendre |
| Έκδοση | 2 |
| Εκδότης | Hilliard and Metcalf, 1825 |
| Πρωτότυπο από | η Δημόσια Βιβλιοθήκη της Νέας Υόρκης |
| Ψηφιοποιήθηκε στις | 21 Ιουν. 2006 |
| Μέγεθος | 224 σελίδες |
| Εξαγωγή αναφοράς | BiBTeX EndNote RefMan |