Elements of Geometry and Trigonometry: With NotesJ. Ryan, 1828 - 316 σελίδες |
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Σελίδα 3
... gles , without having its sides equal . same Art . ) . ( See the The parallelogram , or rhomboid , which has its opposite sides parallel . The lozenge , or rhombus , which has its sides equal , without having its angles right angles ...
... gles , without having its sides equal . same Art . ) . ( See the The parallelogram , or rhomboid , which has its opposite sides parallel . The lozenge , or rhombus , which has its sides equal , without having its angles right angles ...
Σελίδα 6
... gles ACE , ECD : therefore ACD + BCD is the sum of the three angles ACE , ECD , BCD : but the first of those three angles , is a right angle ; and the other two together make up the right angle BCE ; hence the sum of the two angles ACD ...
... gles ACE , ECD : therefore ACD + BCD is the sum of the three angles ACE , ECD , BCD : but the first of those three angles , is a right angle ; and the other two together make up the right angle BCE ; hence the sum of the two angles ACD ...
Σελίδα 7
... gles , C the common vertex , and CD the common side ; then will the exte- rior side CB of the former , and CA A of the latter , be in the same straight line . B For if CB is not the production of AC , let CE be that pro- duction then ...
... gles , C the common vertex , and CD the common side ; then will the exte- rior side CB of the former , and CA A of the latter , be in the same straight line . B For if CB is not the production of AC , let CE be that pro- duction then ...
Σελίδα 8
... gles ; and since AB is a straight line , the sum of the angles ACE , BCE , is also equal to two right angles : hence the sum ACD + ACE is equal to the sum ACE + BCE . Take away from both , the same angle ACE ; there remains the angle ...
... gles ; and since AB is a straight line , the sum of the angles ACE , BCE , is also equal to two right angles : hence the sum ACD + ACE is equal to the sum ACE + BCE . Take away from both , the same angle ACE ; there remains the angle ...
Σελίδα 16
... gles B and E are equal , the side AB - DE , and BG = EF ; hence these triangles are equal ( 36. ) , and consequently AG = DF . Now ( Hyp . ) we have DF = AC ; and therefore AG = AC . But ( 52. ) the oblique line AC cannot be equal to AG ...
... gles B and E are equal , the side AB - DE , and BG = EF ; hence these triangles are equal ( 36. ) , and consequently AG = DF . Now ( Hyp . ) we have DF = AC ; and therefore AG = AC . But ( 52. ) the oblique line AC cannot be equal to AG ...
Άλλες εκδόσεις - Προβολή όλων
Elements Of Geometry And Trigonometry From The Works Of A.m. Legendre Adrien Marie Legendre Δεν υπάρχει διαθέσιμη προεπισκόπηση - 2019 |
Συχνά εμφανιζόμενοι όροι και φράσεις
ABCD adjacent angles altitude angle ACB angle BAD base bisect centre chord circ circle circular sector circumference circumscribed common cone construction continued fraction convex surface cosines cylinder diameter dicular draw drawn equal angles equation equivalent figure formed formulas four right angles frustum given angle given line gles greater homologous sides hypotenuse inclination inscribed intersection isosceles less Let ABC let fall likewise measure multiplied number of sides oblique lines opposite parallel parallelepipedon parallelogram pendicular perimeter perpen perpendicular plane MN polyedron prism proposition quadrilateral radii radius ratio rectangle regular polygon respectively equal right angles right-angled triangle SABC Scholium sector segment similar sine solid angle solid described sphere spherical polygons spherical triangle square straight line suppose tang tangent THEOREM third side three angles trian triangle ABC triangular prism triangular pyramids vertex vertices
Δημοφιλή αποσπάσματα
Σελίδα 257 - The circumference of every circle is supposed to be divided into 360 equal parts, called degrees ; each degree into 60 equal parts, called minutes ; and each minute into 60 equal parts, called seconds.
Σελίδα iii - District, has deposited in this office the title of a book, the right whereof he claims as proprietor, in the words following, to wit : " THE CHILD'S BOTANY," In conformity to the act of the Congress of the United States, 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...
Σελίδα 187 - For, if the arc AD be drawn from the vertex A to the middle point D of the base, the two triangles ABD, ACD, will have all the sides of the one respectively equal to the corresponding sides of the other...
Σελίδα 3 - A right-angled triangle is one which has a right angle. The side opposite the right angle is called the hypothenuse.
Σελίδα 27 - 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 11 - If two triangles have two sides of the one respectively equal to two sides of the other, and the included angles unequal, the triangle which has the greater included angle has the greater third side.
Σελίδα 73 - If two polygons are composed of the same number of triangles, similar each to each, and similarly placed, the polygons are similar. In the two polygons ABCDE and A'B'C'D'E', let the triangles AEB, EEC, CED be similar, respectively, to the triangles A'E'B', B'E'C', C'E'D'; and similarly placed.
Σελίδα 157 - Any two rectangular parallelopipedons are to each other as the products of their bases by their altitudes ; that is to say, as the products of their three dimensions.
Σελίδα 107 - ... of the regular inscribed and circumscribed polygons having double the number of sides. Let AB be a side of the given inscribed polygon ; EF, parallel to AB, a side of the circumscribed polygon ; C the centre of the circle. If the chord AM and the tangents AP, BQ, be drawn, AM...
Σελίδα 59 - Two triangles of the same altitude are to each other as their bases, and two triangles of the same base are to each other as their altitudes. And triangles generally, are to each other, as the products of their bases and altitudes.