. Elements of geometry : containing books I to III. Let ABC be the given A. It is required to describe a 3 about the A. From D and /•.. the middle pts. of AB and AG, draw DO,EO, _ S to Al>. A(. and let them meet in 0. Then . AB is to be a chord of the 0, .. centre of the • lies in DO. III. 1. And . At is to be a 1 hord of the • . .-. centre of the I lies in EO. III. 1. Hence 0 is the centre of the J which can be described? the A, and if a • be described with centre 0 and radiusOA, this will be the © required. Q. E. F. Ex. If BAG be a ri hi angle, show that U will coincidewith the middle poi
. Elements of geometry : containing books I to III. Let ABC be the given A. It is required to describe a 3 about the A. From D and /•.. the middle pts. of AB and AG, draw DO,EO, _ S to Al>. A(. and let them meet in 0. Then . AB is to be a chord of the 0, .. centre of the • lies in DO. III. 1. And . At is to be a 1 hord of the • . .-. centre of the I lies in EO. III. 1. Hence 0 is the centre of the J which can be described? the A, and if a • be described with centre 0 and radiusOA, this will be the © required. Q. E. F. Ex. If BAG be a ri hi angle, show that U will coincidewith the middle point of BG. 136 EU(. LIDS ELEMENTS. [Book III. Proposition XI. Theorem. If ont circle touch . other internally at any point, thecentre i>f the interior circle must lie in that uiius of theoiher circle which passes through that point of Let the © ADE touch the © ABC internally, and let A boa pt. of contact. Find 0 the centre of • .1/<, uiid join : must the centre of • ADE In in the radius .I. For ll I: », let / lie the mitre of • -I //.. Join l. and produce it t meet the ( ce in D and B. Then V / is the centre of © ADE, and from 0 are drawnto the Oce of ADE the st. lines OA, l>. of which l> passesthrough /, .-. OD is greater than OA. III. 8, I or. Bui OA- OB ; ? OD is greater than OB, which is imposfible. /. the centre of • .1 //. is nol oul of the radius OA. .. it lies in (> I. Q. & D. Book III.] PROPOSITION XII. Proposition XII. Theorem. If tiro circles another externally at any paint, (he straight line joining tht ?< nlre of one with tint point of contactmust when p-oduced ijass through the centre of the othr.
Size: 1484px × 1684px
Photo credit: © The Reading Room / Alamy / Afripics
License: Licensed
Model Released: No
Keywords: ., bookcentury1800, bookdecade1880, bookpublish, booksubjectgeometry
