Euclid's Elements of Geometry: From the Latin Translation of Commandine, to which is Added, a Treatise of the Nature and Arithmetic of Logarithms ; Likewise Another of the Elements of Plane and Spherical Trigonometry ; with a Preface ...W. Strahan, 1782 - 399 sider |
Inni boken
Resultat 6-10 av 42
Side 53
... Segments , is equal to double the Rectangle contained under the whole Line , and the faid Segment , together with the Square made of the other Segment . LET the Right Line A B be any how cut in the Point C. I fay the Squares of A B ...
... Segments , is equal to double the Rectangle contained under the whole Line , and the faid Segment , together with the Square made of the other Segment . LET the Right Line A B be any how cut in the Point C. I fay the Squares of A B ...
Side 54
... Segments , is equal to double the Rectangle con- tained under the whole Line , and the faid Segment , to- gether with the Square , made of the other Segment ; which was to be demonftrated . PR POPSITION VIII . THEOREM . If a Right Line ...
... Segments , is equal to double the Rectangle con- tained under the whole Line , and the faid Segment , to- gether with the Square , made of the other Segment ; which was to be demonftrated . PR POPSITION VIII . THEOREM . If a Right Line ...
Side 59
... Segment , fhall be equal to the Square of the other Segment . LE ET AB be a given Right Line . It is required to cut the fame fo , that the Rectangle contained under the Whole , and one Segment thereof , be equal to the Square of the ...
... Segment , fhall be equal to the Square of the other Segment . LE ET AB be a given Right Line . It is required to cut the fame fo , that the Rectangle contained under the Whole , and one Segment thereof , be equal to the Square of the ...
Side 64
... Segment of a Circle is a Figure contained under a Right Line , and a Part of the Circum- ference of a Circle . VII . An Angle of a Segment is that which is contained by a Right Line , and the Circumfe- rence of a Circle . VIII . An ...
... Segment of a Circle is a Figure contained under a Right Line , and a Part of the Circum- ference of a Circle . VII . An Angle of a Segment is that which is contained by a Right Line , and the Circumfe- rence of a Circle . VIII . An ...
Side 65
... Segment , when fome Point is taken in the Circumference thereof , and from it Right Lines are drawn to the Ends of that Right Line , which is the Bafe of the Seg- ment ; then the Angle contained under the Lines , fo drawn , is faid to ...
... Segment , when fome Point is taken in the Circumference thereof , and from it Right Lines are drawn to the Ends of that Right Line , which is the Bafe of the Seg- ment ; then the Angle contained under the Lines , fo drawn , is faid to ...
Vanlige uttrykk og setninger
ABCD adjacent Angles alfo equal alſo Angle ABC Baſe becauſe bifected Centre Circle A B C Circumference Cofine Cone confequently Cylinder defcribed demonftrated Diameter Diſtance drawn equal Angles equiangular Equimultiples faid fame Altitude fame Multiple fame Plane fame Proportion fame Reafon fecond fhall be equal fimilar fince firft folid Parallelopipedon fome fore ftand fubtending given Right Line Gnomon join leffer lefs likewife Logarithm Magnitudes Meaſure Number parallel Parallelogram perpendicular Polygon Prifm Prop PROPOSITION Pyramid Quadrant Ratio Rectangle Rectangle contained remaining Angle Right Angles Right Line A B Right-lined Figure Segment Semicircle ſhall Sides A B Sine Solid Sphere Square Subtangent thefe THEOREM thofe thro tiple Triangle ABC Unity Vertex the Point Wherefore whofe Bafe
Populære avsnitt
Side 193 - If two triangles have two angles of the one equal to two angles of the other, each to each, and one side equal to one side, viz.
Side xxiii - If two triangles have two sides of the one equal to two sides of the other, each to each ; and have likewise the angles contained by those sides equal to each other; they shall likewise have their bases, or third sides, equal; and the two triangles shall be equal; and their other angles shall be equal, each to each, viz. those to which the equal sides are opposite.
Side 236 - 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.
Side 11 - ... sides equal to them of the other. Let ABC, DEF be two triangles which have the two sides AB, AC equal to the two sides DE, DF, each to each, viz. AB equal to DE, and AC to DF ; but...
Side 85 - EA : and because AD is equal to DC, and DE common to the triangles ADE, CDE, the two sides AD, DE are equal to the two CD, DE, each to each ; and the angle ADE is equal to the angle CDE, for each of them is a right angle ; therefore the base AE is equal (4.
Side 147 - A straight line is said to be cut in extreme and mean ratio, when the whole is to the greater segment as the greater segment is to the less.
Side 50 - CB, and to twice the rectangle AC, CB: but HF, CK, AG, GE make up the whole figure ADEB, which is the square of AB ; therefore the square of AB is equal to the squares of AC, CB, and twice the rectangle AC, CB. Wherefore, if a straight line be divided, &c.
Side xxv - EF (Hyp.), the two sides GB, BC are equal to the two sides DE, EF, each to each. And the angle GBC is equal to the angle DEF (Hyp.); Therefore the base GC is equal to the base DF (I.
Side xxxiv - ... therefore their other sides are equal, each to each, and the third angle of the one to the third angle of the other (26.
Side 194 - ABC, and they are both in the same plane, which is impossible ; therefore the straight line BC is not above the plane in which are BD and BE: wherefore, the three straight lines BC, BD, BE are in one and the same plane. Therefore, if three straight lines, &c.